HP 10BII Handleiding

Merk: HP

Model: 10BII

Type: Handleiding

Deze handleiding is ook geschikt voor

10bII Business Calculator

檔名: 10BII_DUTCH(MP01-2)-041029(Print) 頁碼: 第 1/2 頁

hp 10BII Zakelijke Calculator

Gebruikershandboek

Editie 1

HP artikelnummer F1902-90013

檔名: 10BII_DUTCH(MP01-2)-041029(Print) 頁碼: 第 2/2 頁

Mededeling

Het REGISTER JE PRODUCT AAN: www.register.hp.com

DE INHOUD VAN DEZE HANDLEIDING EN DE HIERIN VERVATTE

FICTIEVE PRAKTIJKVOORBEELDEN KUNNEN ZONDER

AANKONDIGING VERANDERD WORDEN. HEWLETT–PACKARD

COMPANY GEEFT GEEN GARANTIE AF VAN WELKE AARD DAN

OOK MET BETREKKING TOT DEZE HANDLEIDING, WAARONDER

OOK STILZWIJGENDE GARANTIES VAN VERHANDELBAARHEID,

GESCHIKTHEID VOOR EEN BEPAALD DOEL EN GEEN INBREUK

VORMEND VAN TOEPASSING ZIJN, MAAR DIE HIER NIET TOT

BEPERKT ZIJN.

HEWLETT–PACKARD CO. KAN NIET AANSPRAKELIJK WORDEN

GESTELD VOOR ENIGERLEI FOUTEN OF VOOR INCIDENTELE OF

GEVOLGSCHADE IN VERBAND MET LEVERING, PRESTATIE OF

GEBRUIK VAN DEZE HANDLEIDING OF DE HIERIN VERVATTE

VOORBEELDEN.

Company, L.P. ermenigvuldiging, aanpassing, of vertaling van deze

handleiding is, behalve zoals toegestaan onder de auteurswet, niet

toegestaan zonder eerder schriftelijke toestemming van Hewlett–Packard

Company.

Hewlett-Packard Company

4995 Murphy Canyon Rd,

Suite 301

San Diego,CA 92123

Oplage

Editie 1 Mei 2003

Welkom bij de HP 10BII 3

Welkom bij de HP 10BII

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10B.book Page 3 Wednesday, June 28, 2000 3:31 PM

4 Welkom bij de HP 10BII

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Eigenschappen

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10B.book Page 4 Wednesday, June 28, 2000 3:31 PM

Inhoud 5

Inhoud

11 In één oogopslag...

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1 23 Om te beginnen

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10B.book Page 5 Wednesday, June 28, 2000 3:31 PM

6 Inhoud

2 33 Economische percentages

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36 0DUJHHQEUXWRZLQVWWHJHOLMNHUWLMGJHEUXLNHQ

3 37 Het opslaan van getallen en rekenkundige

bewerkingen

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37 +HWJHEUXLNYDQFRQVWDQWHQ

39 +HWJHEUXLNYDQKHW0UHJLVWHU

40 +HWJHEUXLNYDQJHQXPPHUGHUHJLVWHUV

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42 5HNHQNXQGLJHEHZHUNLQJHQXLWYRHUHQ

43 0DFKWYHUKHIILQJVRSHUDWRU

43 +HWJHEUXLNYDQKDDNMHVLQEHUHNHQLQJHQ

4 45 Financiële problemen in beeld brengen

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47 (QNHOYRXGLJHUHQWH

48 6DPHQJHVWHOGHUHQWH

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49 7ZHHYHUVFKLOOHQGHILQDQFLsOHYUDDJVWXNNHQ

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51 +HWKHUNHQQHQYDQHHQFDVKIORZYUDDJVWXN

10B.book Page 6 Wednesday, June 28, 2000 3:31 PM

Inhoud 7

5 53 “Time Value of Money”-berekeningen

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55 790UHJLVWHUVZLVVHQ

55 %HJLQHQ(LQGPRGXV

55 +HWEHUHNHQHQYDQOHQLQJHQ

61 %HUHNHQLQJHQPHWVSDDUV\VWHPHQ

64 /HDVHEHUHNHQLQJHQ

68 $PRUWLVDWLH

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6 77 Cashflowberekeningen

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79 &DVKIORZVJURHSHUHQ

80 &DVKIORZVLQYRHUHQ

81 &DVKIORZVEHNLMNHQHQYHUYDQJHQ

82 'HQHWWRKXLGLJHZDDUGHEHUHNHQHQ

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7 87 Statistische berekeningen

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88 6WDWLVWLVFKHJHJHYHQVLQYRHUHQ

88 6WDWLVWLHNHQPHWppQYDULDEHOH

88 6WDWLVWLHNHQPHWWZHH YDULDEHOHQ HQJHZRJHQJHPLGGHOGH

89 6WDWLVWLVFKHJHJHYHQVYHUEHWHUHQ

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89 9HUEHWHUHQYDQJHJHYHQVEHVWDDQGHXLWWZHHYDULDEHOHQ

90 6DPHQYDWWLQJYDQVWDWLVWLVFKHEHUHNHQLQJHQ

91 *HPLGGHOGHVWDQGDDUGGHYLDWLHHQVRPPDWLHVWDWLVWLHNHQ

93 /LQHDLUHUHJUHVVLHHQEHQDGHULQJ

96 *HZRJHQJHPLGGHOGH

10B.book Page 7 Wednesday, June 28, 2000 3:31 PM

8 Inhoud

8 99 Extra voorbeelden

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102 /HQLQJHQH QK \S RWK HNHQ

102 (QNHOYRXGLJHMDDUOLMNV HUHQ WH

102 &RQWLQXHV DPH QV WHOOLQJYDQ UH QWH

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108 /HQLQJP HWHHQ DIZLMNH QGHHHU VWHS HULR GH

109 (HQDXWROHQ LQJ

110 ´&DQDGHVHK\SRWKHHNµ

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113 6SDUHQ

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118 9RRUEHHOGHQ P HWFDVK IOR Z

118 :UDSD UR XQGK \S RWK HNHQ

120 1HWWRWRHNRP VWLJHZD DUGH

A 123 Hulp, Batterijen en Service

123

$QWZRRUGHQRSGHPHHVWYRRUNRPHQGHYUDJHQ

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125 9RHGLQJHQ%DWWHULMHQ

125 %DWWHULMLQGLFDWRU

125 %DWWHULMVSHFLILFDWLHV

126 %DWWHULMHQSODDWVHQ

127 9DVWVWHOOHQRIGHFDOFXODWRUVHUYLFHQRGLJKHHIW

128 %HSHUNWJDUDQWLHEHZLMVYRRUppQMDDU

128 :DWRQGHUGHJDUDQWLHYDOW

129 :DWQLHWRQGHUGHJDUDQWLHYDOW

129 .ODQWHQWUDQVDFWLHVLQKHW9HUHQLJG.RQLQNULMN

130 $OVGHFDOFXODWRUVHUYLFHQRGLJKHHIW

10B.book Page 8 Wednesday, June 28, 2000 3:31 PM

Inhoud 9

130 6HUYLFHDGUHVVHQ

130 6HUYLFHNRVWHQ

131 9HU]HQGLQVWUXFWLHV

131 *DUDQWLHRSVHUYLFH

131 6HUYLFHFRQWUDFWHQ

132 9HUGHUHLQIRUPDWLH

133 7HUPHQHQFRQGLWLHVYRRUGHHLQGJHEUXLNHU

B 135 Nog meer berekeningen

135

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135 0RJHOLMNHUHVXOWDWHQELMKHWEHUHNHQ HQYDQ,55<5

136 ,55<5VWRSSHQHQRSQLHXZEHJLQQHQ

136 (HQVFKDWWLQJLQYRHUHQYR RU,55<5

137 *HYROJHQYDQKHWJHEUXLNYDQ 

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137 *HWDOOHQEHUHLN

138 )RUPXOHV

138 %HUHNHQLQJYDQPDUJHHQEUXWRZLQVW

138 7LPH9DOXHRI0RQH\790

139 $PRUWLVDWLH

139 5HQWHYRHWFRQYHUVLHV

140 &DVKIORZEHUHNHQLQJHQ

141 6WDWLVWLHN

C 143 Meldingen

145 Index

10B.book Page 9 Wednesday, June 28, 2000 3:31 PM

10B.book Page 10 Wednesday, June 28, 2000 3:31 PM

11In één oogopslag...

In één oogopslag...

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=HWGHFDOFXODWRUDDQ

[oranje label] 0,00

7RRQWGHVKLIWLQGLFDWRU



SHIFT

0,00

*DDWZHHUXLWGHVKLIW

LQVWHOOLQJ

12_

:LVWKHWODDWVWHWHNHQ

0,00

:LVWGHGLVSOD\

0,00

:LVWKHWVWDWLVWLVFKH

JHKHXJHQ

0,00

:LVWKHWKHOHJHKHX

JHQ

=HWGHFDOFXODWRUXLW

10B.book Page 11 Wednesday, June 28, 2000 3:31 PM

12 In één oogopslag...

Procenten—In één oogopslag...

7HOELMRS

%HUHNHQGHPDUJHDOVGHNRVWHQJHOLMN]LMQDDQHQGHYHUNRRSSULMV

LV

$OVGHNRVWHQ]LMQHQGHEUXWRZLQVWLVZDWLVGDQGH

YHUNRRSSULMV"

3URFHQW

.RVWHQ

3ULMV

0DUJH

%UXWRZLQVW

Toetsen: Display: Beschrijving:

17,50

9RHUWJHWDOLQ

20,13

7HOWRS

15,00

9RHUWGHNRVWHQLQ

22,00

9RHUWGHSULMVLQ

31,82

%HUHNHQWGHPDUJH

20,00

9RHUWGHNRVWHQLQ

33,00

9RHUWGHEUXWRZLQVWLQ

26,60

%HUHNHQWGHSULMV

10B.book Page 12 Wednesday, June 28, 2000 3:31 PM

In één oogopslag... 13

Geheugentoetsen—In één oogopslag…

9HUPHQLJYXOGLJHQPHWZDDUELM´ïµDOVHHQEHZHUNLQJPHW

HHQFRQVWDQWHZRUGWRSJHVODJHQ

6ODLQUHJLVWHURSHQYUDDJKHWYHUYROJHQVRS

6ODDWHHQEHZHUNLQJPHWHHQFRQVWDQWHRS

6ODDWHHQZDDUGHRSLQKHW0UHJLVWHUJHKHXJHQSODDWV

9UDDJWHHQZDDUGHRSXLWKHW0UHJLVWHU

7HOWHHQZDDUGHRSELMKHWJHWDOGDWLQKHW0UHJLVWHULV

RSJHVODJHQ

6ODDWHHQZDDUGHRSLQHHQJHQXPPHUGUHJLVWHU

9UDDJWHHQZDDUGHRSXLWHHQJHQXPPHUGUHJLVWHU

Toetsen: Display: Beschrijving:

7,00

6ODDW´ïµDOVHHQ

EHZHUNLQJPHWHHQFRQVWDQWH

RS

119,00

9HUPHQLJYXOGLJWï

154,00

9HUPHQLJYXOGLJWï

175,00

9HUPHQLJYXOGLJWï

519,00

6ODDWLQUHJLVWHURS

0,00

:LVWGHGLVSOD\

519,00

9UDDJWUHJLVWHURS

10B.book Page 13 Wednesday, June 28, 2000 3:31 PM

14 In één oogopslag...

Time Value of Money (TVM)—In één

oogopslag…

9RHUYLHUZLOOHNHXULJHZDDUGHQLQHQEHUHNHQGHYLMIGH

ZDDUGH

(HQPLQWHNHQLQGHGLVSOD\EHWHNHQWHHQEHWDDOGEHGUDJKHW

RQWYDQJHQEHGUDJLVSRVLWLHI

$OVX39JHGXUHQGHPDDQGHQOHHQW1WHJHQHHQUHQWH

YDQ,<5KRHJURRW]LMQGDQGHPDDQGHOLMNVHEHWDOLQJHQ"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

$DQWDOEHWDOLQJHQ

5HQWHSHUMDDU

+XLGLJHZDDUGH

%HWDOLQJ

7RHNRPVWLJHZDDUGH

%HJLQRI(LQGPRGXV

´$DQWDOEHWDOLQJHQSHUMDDUµPRGXV

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

360,00

9RHUWKHWDDQWDOEHWDOLQJHQLQ

10,00

9RHUWGHUHQWHSHUMDDULQ

14.000,00

9RHUWGHKXLGLJHZDDUGHLQ

0,00

9RHUWGHWRHNRPVWLJHZDDUGH

LQ

–122,86

%HUHNHQWGHEHWDOLQJDOVGH]H

DDQKHWHLQGHYDQGHSHULRGH

ZRUGWEHWDDOG

10B.book Page 14 Wednesday, June 28, 2000 3:31 PM

In één oogopslag... 15

TVM Wat gebeurt er als…—In één oogopslag…

+HWLVQLHWQRGLJGDWYRRULHGHUYRRUEHHOGGH790ZDDUGHQ

RSQLHXZZRUGHQLQJHYRHUG+RHYHHONXQWXOHQHQPHWGH

ZDDUGHQGLHX]RMXLVWKHEWLQJHYRHUGSDJLQD DOVX

EHWDOLQJHQYDQZLOWGRHQ"

+RHYHHONXQWXOHQHQWHJHQHHQUHQWHYDQ"

Toetsen: Display: Beschrijving:

–100,00

9RHUWKHWQLHXZH

EHGUDJYDQGHEHWDOLQJ

LQ+HWXLWEHWDDOGH

EHGUDJLVQHJDWLHI

11.395,08

%HUHNHQWKHWEHGUDJ

GDWXNXQWOHQHQ

9,50

9RHUWGHQLHXZHUHQW

HYRHWLQ

11.892,67

%HUHNHQWGHQLHXZH

KXLGLJHZDDUGHYRRU

HHQEHWDOLQJYDQ

ELMHHQUHQWH

YDQ

10,00

9RHUWGH

RRUVSURQNHOLMNHUHQWH

RSQLHXZLQ

14.000,00

9RHUWGHRRU

VSURQNHOLMNHKXLGLJH

ZDDUGHRSQLHXZLQ

–122,86

%HUHNHQWGH

RRUVSURQNHOLMNH

EHWDOLQJ

10B.book Page 15 Wednesday, June 28, 2000 3:31 PM

16 In één oogopslag...

Amortisatie—In één oogopslag…

1DKHWEHUHNHQHQYDQHHQEHWDOLQJPHW7LPH9DOXHRI

0RQH\790YRHUWXGHSHULRGHVLQZDDULQ

JHDPRUWLVHHUGZRUGWHQGUXNWXYHUYROJHQVRS



'UXNGDQRS

RPGHUHQWHKRRIGVRPHQVDOGRZDDUGHQ

WHEHNLMNHQUHVSHFWLHYHOLMNDDQJHGXLGGRRUGH

PRININT

HQ

BALLQGLFDWRU

$PRUWLVHHUPHWEHKXOSYDQKHWYRULJH790YRRUEHHOGSDJLQD HHQ

HQNHOYRXGLJHEHWDOLQJHQYHUYROJHQVHHQUHHNVEHWDOLQJHQ

$PRUWLVHHUGH

EHWDOLQJYDQGHOHQLQJ

$PRUWLVHHUGH

WRWHQPHWGH EHWDOLQJHQYDQGHOHQLQJ

Toetsen: Display: Beschrijving:

20,00

9RHUWGHEHWDOLQJLQGLHPRHW

JHDPRUWLVHHUGZRUGHQ

20 – 20

*HHIWGHEHWDOLQJZHHUGLH

PRHWJHDPRUWLVHHUGZRUGHQ

–7,25

*HHIWGHKRRIGVRPZHHU

–115,61

*HHIWGHUHQWHZHHU%HWDDOGH

EHGUDJHQ]LMQQHJDWLHI

13.865,83

*HHIWKHWVDOGRZHHU

12_

9RHUWGHUHHNVEHWDOLQJHQLQ

GLHPRHWHQJHDPRUWLVHHUG

ZRUGHQ

1 – 12

*HHIWGHUHHNVYDQSHULRGHV

EHWDOLQJHQZHHU

–77,82

*HHIWGHKRRIGVRPZHHU

–1.396,50

*HHIWGHUHQWHZHHU%HWDDOGH

EHGUDJHQ]LMQQHJDWLHI

13.922,18

*HHIWKHWVDOGRZHHU

10B.book Page 16 Wednesday, June 28, 2000 3:31 PM

In één oogopslag... 17

Rentevoetconversies—In één oogopslag…

2PWHFRQYHUWHUHQWXVVHQGHQRPLQDOHHQHIIHFWLHYHUHQWH

YRHUWXGHEHNHQGHUHQWHHQKHWDDQWDOSHULRGHVSHUMDDULQ

HQEHUHNHQWXYHUYROJHQVGHRQEHNHQGHUHQWH

%HUHNHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYDQHHQQRPLQDOHUHQWHYDQGLH

PDDQGHOLMNVVDPHQJHVWHOGZRUGW

1RPLQDDOUHQWHSHUFHQWDJH

(IIHFWLHIUHQWHSHUFHQWDJH

3HULRGHVSHUMDDU

Toetsen: Display: Beschrijving:

10,00

9RHUWGHQRPLQDOH

UHQWHLQ

12,00

9RHUWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

10,47

%HUHNHQWGHMDDUOLMNVH

HIIHFWLHYHUHQWH

10B.book Page 17 Wednesday, June 28, 2000 3:31 PM

18 In één oogopslag...

IRR/YR en NPV—In één oogopslag…

:DWLVGH,55<5DOVXHHQLQLWLsOHXLWJDDQGHFDVKIORZKHEWYDQ

JHYROJGGRRUPDDQGHOLMNVLQNRPHQGHFDVKIORZVYDQ

HQ":DWLVGH,55SHUPDDQG"

:DWLVGH139DOVGHGLVFRQWRUHQWHLV"

$DQWDOSHULRGHVSHUMDDUVWDQGDDUGZDDUGHLV

&DVKIORZVPD[LPDDO´MµJHHIWKHWQXPPHUYDQGHFDVK

IORZJURHSDDQ

$DQWDONHUHQGDWFDVKIORZ´MµDFKWHUHHQYROJHQVYRRUNRPW

,QWHUQUHQGHPHQWSHUMDDU

1HWWRFRQWDQWHZDDUGH

Toetsen: Display: Beschrijving:

0,00

:LVWKHWKHOHJHKHXJHQ

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

–40.000,00

9RHUWGHLQLWLsOHXLWJDDQGH

FDVKIORZLQ

4.700,00

9RHUWGHHHUVWHFDVKIORZLQ

7.000,00

9RHUWGHWZHHGHFDVKIORZLQ

2,00

9RHUWLQKRHYDDNGHFDVK

IORZDFKWHUHHQYROJHQV

YRRUNRPW

23.000,00

9RHUWGHGHUGHFDVKIORZLQ

15,96

%HUHNHQW,55<5

1,33

%HUHNHQW,55SHUPDDQG

10 10,00

9RHUW,<5LQ

622,85

%HUHNHQW139

10B.book Page 18 Wednesday, June 28, 2000 3:31 PM

In één oogopslag... 19

Statistiek—In één oogopslag…

%HUHNHQPHWEHKXOSYDQGHYROJHQGHJHJHYHQVKHWJHPLGGHOGHYDQ[HQ\

GHVWHHNSURHIVWDQGDDUGGHYLDWLHYRRU[ HQ\HQKHWVQLMSXQWPHWGH\DV

HQGHULFKWLQJVFRsIILFLsQWYDQGHOLMQGLHGHOLQHDLUHUHJUHVVLHZHHUJHHIW

%HUHNHQYHUYROJHQVPHWVRPPDWLHVWDWLVWLHNHQQHQ

[\

:LVWVWDWLVWLVFKHUHJLVWHUV

JHWDO

9RHUWVWDWLVWLVFKHJHJHYHQVPHWppQYDULDEHOHLQ

JHWDO

9HUZLMGHUWVWDWLVWLVFKHJHJHYHQVPHWppQYDULD

EHOH

JHWDO

JHWDO 9RHUWVWDWLVWLVFKHJHJHYHQVPHWWZHHYDULDEHOHQ

LQ

JHWDO

JHWDO 9HUZLMGHUWVWDWLVWLVFKHJHJHYHQVPHWWZHHYDULD

EHOHQ

*HPLGGHOGHQYDQ[HQ\

*HPLGGHOGHYDQ[JHZRJHQGRRU\

6WHHNSURHIVWDQGDDUGGHYLDWLHYRRU[HQ\

3RSXODWLHVWDQGDDUGGHYLDWLHYRRU[HQ\

\ZDDUGH

%HQDGHULQJYDQ[HQGHFRUUHODWLHFRsIILFLsQW

[ZDDUGH

%HQDGHULQJYDQ\

6QLMSXQWPHWGH\ DVHQGHKHOOLQJ

-gegevens 2 4 6

-gegevens 50 90 160

10B.book Page 19 Wednesday, June 28, 2000 3:31 PM

20 In één oogopslag...

Toetsen: Display: Beschrijving:

0,00

:LVWGHVWDWLVWLVFKHUHJLVWHUV

1,00

9RHUWKHWHHUVWH[\SDDULQ

2,00

9RHUWKHWWZHHGH[\SDDULQ

3,00

9RHUWKHWGHUGH[\SDDULQ

4,00

*HHIWKHWJHPLGGHOGHYDQGH[

ZDDUGHQZHHU

100,00

*HHIWKHWJHPLGGHOGHYDQGH\

ZDDUGHQZHHU

2,00

*HHIWGHVWHHNSURHIVWDQGDDUG

GHYLDWLHYRRU[ZHHU

55,68

*HHIWGHVWHHNSURHIVWDQGDDUG

GHYLDWLHYRRU\ZHHU

–10,00

*HHIWKHWVQLMSXQWYDQGH

UHJUHVVLHOLMQPHWGH\DVZHHU

EHQDGHUGH ZDDUGHYRRU

[ 

27,50

*HHIWGHKHOOLQJYDQGHUHJUHVV

LHOLMQZHHU

3,00

*HHIWQKHWDDQWDOLQJHYRHUGH

JHJHYHQVZHHU

1.420,00

*HHIW

[\VRPYDQGH

SURGXFWHQYDQ[HQ\ZDDUGHQ

10B.book Page 20 Wednesday, June 28, 2000 3:31 PM

In één oogopslag... 21

Toetsen

1. Time value of money (pagina 53)

2. Twee getallen scheiden

(pagina 28)

3. Procent (pagina 33)

4. Constanten (pagina 37)

5. Opslaan en opvragen (pagina 40)

6. Teken veranderen (pagina 24)

7. Statistiektoets (pagina 28)

8. Shifttoets (pagina 27)

9. Display wissen, bewerking

annuleren (pagina 25)

10. Gehele geheugen wissen

(pagina 25)

11. Aan (pagina 23)

12. Statistische functies (pagina 90)

13.

tot en met

: registers voor

sommatiestatistieken (pagina 91)

14. 3-toetsen geheugen (pagina 39)

15. Backspace (pagina 25)

16. Statistische gegevens

accumuleren (pagina 88)

17. Cashflows (pagina 77)

18. Economische functies: marge,

brutowinst, kosten, prijs

(pagina 35)

19. Renteconversies (pagina 73)

20. Amortisatie (pagina 68)

21. Indicator regel (pagina 26)

10B.book Page 21 Wednesday, June 28, 2000 3:31 PM

10B.book Page 22 Wednesday, June 28, 2000 3:31 PM

1: Om te beginnen 23

Om te beginnen

Aan- en uitzetten

8]HWXZ+3%,,DDQGRRURS WHGUXNNHQ8]HWGH

FDOFXODWRUXLWGRRURSGHRUDQMHVKLIWWRHWV

WHGUXNNHQ

HQYHUYROJHQVRS

WHGUXNNHQZRUGWRRNDOVYROJW

DDQJHJHYHQ



$DQJH]LHQGHFDOFXODWRUHHQSHUPDQHQWJHKHXJHQKHHIW

ZRUGWGHRSJHVODJHQLQIRUPDWLHQLHWDDQJHWDVWDOVGH

FDOFXODWRUXLWJH]HWZRUGW2PVWURRPWHEHVSDUHQVFKDNHOWGHFDOFXODWRU

]LFK]HOIRQJHYHHUPLQXWHQQDGDWKLMYRRUKHWODDWVWJHEUXLNWZHUGXLW

'HFDOFXODWRUJHEUXLNWWZHHOLWKLXPEDWWHULMHQ$OVXKHWV\PERROYRRU

ODJHEDWWHULMVSDQQLQJ LQGHGLVSOD\]LHWPRHWHQGHEDWWHULMHQ

ZRUGHQYHUYDQJHQ5DDGSOHHJDDQKDQJVHO$YRRUPHHULQIRUPDWLH

De helderheid van de display aanpassen

2PGHKHOGHUKHLGYDQGH GLVSOD\WHY HUDQGHUHQKRXGWX LQJHGUXNWHQ

GUXNWXWHJHOLMNHUWLMGRS

RI 

Eenvoudige rekenkundige berekeningen

Rekenkundige operatoren. ,QGHYROJHQGHYRRUEHHOGHQ]LHWXKHW

JHEUXLNYDQGHUHNHQNXQGLJHRSHUDWRUHQ

  HQ 

$OVXDFKWHUHHQYROJHQVRSPHHUGDQppQRS HUDWRUGUXNWELMYRRUEHHOGRS

    ZRUGWHQNHOPHWGHODDWVWJHGUXNWHWRHWVUHNHQLQJ

JHKRXGHQ

10B.book Page 23 Wednesday, June 28, 2000 3:31 PM

24 1: Om te beginnen

$OVXELMKHWLQYRHUHQYDQHHQJHWDOHHQW\SHIR XWPDDNWGUXNGDQRS 

RP]RGHIRXWLHYHFLMIHUVWHZLVVHQ

$OVHHQEHUHNHQLQJDIJHVORWHQLVGRRU

LQWHGUXNNHQEHJLQWGRRUKHW

LQGUXNNHQYDQHHQFLMIHUWRHWVHHQQLHXZHEHUHNHQLQJ

$OVXQDGDWXGHEHUHNHQLQJKHEWXLWJHYRHUGRSHHQRSHUDWRUWRHWVGUXNW

NXQWXYHUGHUJDDQPHWGHEHUHNHQLQJ

8NXQWNHWWLQJEHZHUNLQJHQXLWYRHUHQGRRUQLHWQDLHGHUHVWDSRS

WH

GUXNNHQ

.HWWLQJEHZHUNLQJHQZRUGHQJHwQWHUSUHWHHUGLQGHYROJRUGHZDDURS]LM

ZRUGHQLQJHYRHUG%HUHNHQ[

Negatieve getallen. 9RHUKHWJHWDOLQHQGUXNRS DOVXKHWWHNHQZLOW

YHUDQGHUHQ%HUHNHQ²¸

Toetsen: Display: Beschrijving:

87,18

7HOWHQRS

240,92

%HUHNHQWï

356,42

6OXLWGHEHUHNHQLQJYDQ

DI

36,92

'RRURS WHGUXNNHQ

NRPWGHWXVVHQRSORVV

LQJ ïLQGH

GLVSOD\

40,57

'HEHZHUNLQJLVNODDU

13,00

7HOWRS

39,00

9HUPHQGLJYXOGLJWï



Toetsen: Display: Beschrijving:

–75_

9HUDQGHUWKHWWHNHQ

YDQ

–25,00

%HUHNHQWKHWUHVXOWDDW

10B.book Page 24 Wednesday, June 28, 2000 3:31 PM

1: Om te beginnen 25

De display en het toetsenbord begrijpen

Cursor

8]LHWGHFXUVRUBDOVXHHQJHWDOLQYRHUW

Het wissen van de calculator

$OVGHFXUVRULQGHGLVSOD\VWDDWZRUGWGRRU KHWODDWVW

LQJHYRHUGHFLMIHUJHZLVW,QDOOHDQGHUHJHYDOOHQZRUGWGRRU

GHGLVSOD\JHZLVWHQGHEHZHUNLQJJHDQQXOHHUG

$OVXRS

GUXNWELMKHWLQYRHUHQYDQHHQJHWDONRPWLQ

GHGLVSOD\WHVWDDQ$QGHUVZLVW

GHJHJHYHQVGLHLQGH

GLVSOD\VWDDQHQZRUGWGHKXLGLJHEHZHUNLQJJHDQQXOHHUG

Meldingen verwijderen.$OVGH+3%,,HHQIRXWPHOGLQJWRRQW

YHUZLMGHUWXGHPHOGLQJPHW

RIPHW HQNULMJWXGHRRUVSURQNHOLMNH

LQKRXGZHHULQGHGLVSOD\WH]LHQ=LH´0HOGLQJHQµRSSDJLQD YRRU

HHQYROOHGLJHOLMVWYDQPHOGLQJHQHQKXQEHWHNHQLV

Het geheugen wissen

Toetsen Beschrijving

:LVWKHWKHOHJHKHXJHQ6WHOWGHLQVWHOOLQJHQQLHW

RSQLHXZLQ

:LVWKHWVWDWLVFKHJHKHXJHQ

10B.book Page 25 Wednesday, June 28, 2000 3:31 PM

26 1: Om te beginnen

2PKHWJHKHOHJ HKHXJ HQWHZLVVHQ HQRP GHFDOFXODWRURSQ LHXZLQWH

VWHOOHQGUXNWXRS 

KRXGWXGH]HLQJHGUXNWZDDUQDXWHJHOLMNHUWLMGRS

HQ GUXNWHQGH]HHYHQHHQVLQJHGUXNWKRXGW$OVXGHGULHWRHWVHQ

ORVODDWLVKHWJHKHOHJHKHXJHQJHZLVW2SGHGLVSOD\YHUVFKLMQWGH

PHOGLQJ

All Clear

Indicators

,QGLFDWRUV]LMQV\PEROHQLQGHGLVSOD\GLHGHVWDWXVYDQGHFDOFXODWRU

DDQJHYHQ

Indicator Status

SHIFT 'HVKLIWWRHWV  ZHUGLQJHGUXNW$OVXHHQDQGHUH

WRHWVLQGUXNWZRUGWGHIXQFWLHGLHERYHQGHWRHWV

LQKHWRUDQMHLVDDQJHJHYHQXLWJHYRHUG

STATS 'HVWDWLVWLHNWRHWV LVDFWLHI$OVXHHQDQGHUH

WRHWVLQGUXNWZRUGWGHIXQFWLHXLWJHYRHUGGLHERYHQ

GHWRHWVLQKHWSDDUVLVDDQJHJHYHQ

PEND (UPRHWYRRUGHEHZHUNLQJQRJHHQRSHUDQG

ZRUGHQLQJHYRHUG

BEGIN 'H%HJLQPRGXVLVDFWLHISDJLQD GHEHWDOLQJHQ

JHEHXUHQDDQKHWEHJLQYDQHHQSHULRGH

INPUT 'H WRHWVZHUGLQJHGUXNWHQHUZHUGHHQQXP

PHURSJHVODJHQ

'HEDWWHULMHQ]LMQELMQDOHHJSDJLQD 

AMORT 'HDPRUWLVDWLHLQGLFDWRULV]LFKWEDDUVDPHQPHW

ppQYDQGHYROJHQGHYLHULQGLFDWRUV

BAL +HWVDOGRYDQHHQDPRUWLVDWLHZRUGWZHHUJH

JHYHQSDJLQD 

INT 'HUHQWHYDQHHQDPRUWLVDWLHZRUGWZHHUJH

JHYHQSDJLQD 

PRIN 'HKRRIGVRPYDQHHQDPRUWLVDWLHZRUGWZHHUJH

JHYHQSDJLQD 

PER (UZRUGWHHQ DDQWDOSHULRGHVJHEUXLNWYRRUHHQ

DPRUWLVDWLHSDJLQD 

C-FLOW 'HFDVKIORZLQGLFDWRULV]LFKWEDDUVDPHQPHWppQ

YDQGHYROJHQGHWZHHLQGLFDWR UV

10B.book Page 26 Wednesday, June 28, 2000 3:31 PM

1: Om te beginnen 27

Shifttoets

9RRUELMQDDOOHWRHWVHQYDQGH+3%,,EHVWDDWHHQ

WZHHGH´VKLIWHGµIXQFWLHGLHLQKHWRUDQMHERYHQGH

EHWUHIIHQGHWRHWVVWDDW0HWGHRUDQMHVKLIWWRHWV

NULMJW

XWRHJDQJWRWGH]HIXQFWLHV

$OVXRS

GUXNWNULMJWXGHVKLIWLQGLFDWRUSHIFTWH

]LHQZDDUPHHZRUGWDDQJHJHYHQGDWGHVKLIWHGIXQFWLHV

DFWLHI]LMQ'H

SHIFTLQGLFDWRU]HWXXLWGRRUZHHURS 

WHGUXNNHQ

8GUXNWELMYRRUEHHOGRS

HQYHUYROJHQVRS HYHQHHQVDOV 

DDQJHJHYHQRPKHWJHWDOLQGHGLVSOD\PHW]LFK]HOIWHYHUPHQLJYXOGLJHQ

CF +HWQXPPHUYDQGHFDVKIORZLVNRUW]LFKWEDDU

ZDDUQDGHFDVKIORZZRUGWZHHUJHJHYHQ

N +HWQXPPHUYDQGHFDVKIORZLVNRUW]LFKWEDDU

ZDDUQDKHWDDQWDONHUHQGDWHHQFDVKIORZDFKW

HUHHQYROJHQVYRRUNRPWZRUGWZHHUJHJHYHQ

ERROR 'HIRXWLQGLFDWRULV]LFKWEDDUVDPHQPHWppQYDQ

GHYROJHQGHYLHULQGLFDWRUV

TVM (ULVHHQ790IRXWELMYRRUEHHOGRSORVVHQQDDU

3<5

FULL (UZHUGHQPHHUGDQFDVKIORZVLQJHYRHUGRIHU

ZHUGHQPHHUGDQQLHWRSJHORVWHKDDNMHVJHEUXLNW

STAT )RXWLHYHGDWDJHEUXLNWLQHHQVWDWLVWLVFKHEHUHNHQ

LQJRILQGLHQQLHWZHHUJHJHYHQZRUGWHUZHUGHHQ

VWDWLVWLVFKHEHUHNHQLQJXLWJHYRHUG

FUNC (ULVHHQZLVNXQGLJHIRXWJHEHXUGELMYRRUEHHOG

GHOHQGRRUQXO

STAT (UZHUGHHQVWDWLVWLVFKHEHUHNHQLQJXLWJHYRHUG

Indicator Status

10B.book Page 27 Wednesday, June 28, 2000 3:31 PM

28 1: Om te beginnen

Statistiektoets

'HVWDWLVWLHNWRHWV SDDUVJHNOHXUGZRUGWJHEUXLNWRP

WRHJDQJWHNULMJHQWRWVRPPDWLHVWDWLVWLHNHQXLWGH

VWDWLVWLVFKHJHKHXJHQUHJLVWHUV

$OVXRS

GUXNWNULMJWXGHVWDWLVWLHNLQGLFDWRUSTATSWH

]LHQ'LWEHWHNHQWGDWXppQYDQGH]HV

VRPPDWLHVWDWLVWLHNHQNXQWRSURHSHQPHWGHYROJHQGH

WRHWVDDQVODJ]LHSDJLQD 

%LMYRRUEHHOGGUXNRS

HQYHUYROJHQVRS RPGHVRPYDQGH

LQJHYRHUGH [ ZDDUGHQRSWHURHSHQ

INPUT-toets

'H WRHWVZRUGWJHEUXLNWRPWZHHJHWDOOHQWHVFKHLGHQ

DOVXZHUNWPHWHHQIXQFWLHPHWWZHHYDULDEHOHQRIPHW

VWDWLVWLHNHQPHWWZHHYDULDEHOHQ'H

WRHWVNDQRRN

ZRUGHQJHEUXLNWRPHHQZLVNXQGLJHEHZHUNLQJDOWLMGHQGH

YHUZHUNLQJWHHYDOXHUHQLQGLWJHYDONULMJWXKHW]HOIGH

UHVXOWDDWDOVGRRUKHWLQGUXNNHQYDQ



SWAP-toets

'RRURS WHGUXNNHQZRUGWKHWYROJHQGHYHUZLVVHOG

'HODDWVWHWZHHJHWDOOHQGLH]LMQLQJHYRHUGRP

ELMYRRUEHHOGELMGHOHQHQDIWUHNNHQGHYROJRUGHWH

YHUDQGHUHQ

'HRSORVVLQJHQYDQHHQIXQFWLHGLHWZHHZDDUGHQ

EHUHNHQW

'H[HQ\ZDDUGHQELMVWDWLVWLVFKHWRHSDVVLQJHQ

10B.book Page 28 Wednesday, June 28, 2000 3:31 PM

1: Om te beginnen 29

Wiskundige functies

Functies met één onbekende. :LVNXQGLJHIXQFWLHV

ZDDUppQRQEHNHQGHLQYRRUNRPWJHEUXLNHQKHWJHWDOLQGH

GLVSOD\DOVRQEHNHQGH

Functies met twee onbekenden. $OVHUYRRUHHQ

IXQFWLHWZHHJHWDOOHQQRGLJ]LMQZRUGHQGH]HDOVYROJW

LQJHYRHUGJHWDO

JHWDOHQYHUYROJHQVGHXLWWHYRHUHQ

EHZHUNLQJ$OVXRS

GUXNWZRUGWGHKXLGLJH

XLWGUXNNLQJEHUHNHQGHQ]LHWXGH

INPUTLQGLFDWRU'RRU

GHYROJHQGHWRHWVDDQVODJHQZRUGWELMYRRUEHHOGGH

SURFHQWXHOHYHUDQGHULQJWXVVHQHQEHUHNHQG

Toetsen: Display: Beschrijving:

9,45

%HUHNHQWGHYLHU

NDQWVZRUWHO

0,42

ZRUGWHHUVW

EHUHNHQG

3,99

7HOWHQELM

HONDDURS

Toetsen: Display: Beschrijving:

17,00

9RHUWJHWDOLQGH

INPUTLQGLFDWRUYHU

VFKLMQW

29_

9RHUWJHWDOLQ

70,59

%HUHNHQWGHSURFHQWXHOH

YHUDQGHULQJ

10B.book Page 29 Wednesday, June 28, 2000 3:31 PM

30 1: Om te beginnen

Het formaat van getallen tonen

$OVXGH+3%,,YRRUKHWHHUVWDDQ]HWZRUGHQJHWDOOHQ

LQWZHHGHFLPDOHQQDXZNHXULJJHWRRQGPHWHHQGHFLPDOH

SXQW+HWDDQWDOFLMIHUVGDWXLQGHGLVSOD\]LHWZRUGW

EHSDDOGGRRUGHJHWDOQRWDWLH

$OVKHWUHVXOWDDWYDQHHQEHUHNHQLQJHHQJHWDOLVPHWPHHU

VLJQLILFDQWHFLMIHUVGDQLQGHKXLGLJHQRWDWLHNDQZRUGHQ

JHWRRQGZRUGWKHWJHWDODIJHURQG]RGDWKHWLQGHKXLGLJHGLVSOD\

LQVWHOOLQJSDVW

2QJHDFKWGHKXLGLJHGLVSOD\QRWDWLHZRUGWLHGHUJHWDORSJHVODJHQDOVHHQ

FLMIHULJJHWDOGDWYDQHHQWHNHQLVY RRU]LHQPHWHHQGULHFLMIHULJH

H[SRQHQWRRNYDQHHQWHNHQYRRU]LHQ

Het aantal getoonde decimalen aangeven

*DDOVYROJWWHZHUNRPKHWDDQWDOJHWRRQGHGHFLPDOHQDDQ WHJHYHQ

 'UXNRS



 9RHUKHWDDQWDOGHFLPDOHQWPLQGDWXZLOW]LHQ

$OVHHQJHWDOWHJURRWRIWHNOHLQLVRPLQKHW',63IRUPDDWJHWRRQGWH

ZRUGHQZRUGWKHWDXWRPDWLVFKLQGHZHWHQV FKDSSHOLMNHQRWDWLHJHWRRQG

Toetsen: Display: Beschrijving:

0,00

:LVWGHGLVSOD\

0,000

7RRQWGULHGHFLPDOHQ

5,727

5,727360000

7RRQWQHJHQGHFL

PDOHQ

5,73

7HUXJQDDUGHQRWDWLH

PHWWZHHGHFLPDOHQ

+HWJHWDOLQGHGLVSOD\

ZRUGWDIJHURQG

10B.book Page 30 Wednesday, June 28, 2000 3:31 PM

1: Om te beginnen 31

Wetenschappelijke notatie

'HZHWHQVFKDSSHOLMNHQRWDWLHZRUGWJHEUXLNWYRRUJHWDOOHQ

GLHWHJURRWRIWHNOHLQ]LMQYRRUGHGLVSOD\$OVX

ELMYRRUEHHOGKHWJHWDO

 

LQYRHUWLVKHWUHVXOWDDW(GDWEHWHNHQWppQNHHU

WLHQWRWGHYHHUWLHQGHPDFKWRIZDDUELMGHGHFLPDOH

NRPPDYHHUWLHQSODDWVHQ QDDUUHFKWVZRUGWJHVFKRYHQ8

NXQWGLWJHWDOLQYRHUHQGRRU

LQWHWRHWVHQ'H(

EHWHNHQWGH´H[SRQHQWYDQWLHQµ

9RRU]HHUNOHLQHJHWDOOHQNXQQHQH[SRQHQWHQRRNQHJDWLHIZRUGHQ+HW

JHWDO]LHWXDOV(²GLWEHWHNHQWYLHUNHHUWLHQWRW

GHQHJDWLHYHWZDDOIGHPDFKWRI´ZDDUELMGHGHFLPDOHNRPPD

SODDWVHQQDDUOLQNVLVYHUVFKRYHQµ8NXQWGLWJHWDOLQYRHU HQGRRU

LQWHWRHWVHQ

Getallen met volledige nauwkeurigheid tonen

'RRURS WHGUXNNHQVWHOWXGHFDOFXODWRULQRP

JHWDOOHQ]RQDXZNHXULJPRJHOLMNWHWRQ HQQXOOHQDFKWHU

KHWJHWDOZRUGHQQLHWJHWRRQG$OVXWLMGHOLMNDOOHFLMIHUV

YDQKHWJHWDOLQGHGLVSOD\ZLOWEHNLMNHQRQDIKDQNHOLMNYDQ

GHLQJHVWHOGHJHWDOQRWDWLHGUXNWXRS

HQKRXGWX

LQJHGUXNW8]LHWKHWJHWDO]RODQJX LQJHGUXNWKRXGW

'HGHFLPDOHNRPPDZRUGWQLHWJHWRRQG

%HJLQPHWWZHHGHFLPDOHQ



Punt en komma verwisselen

8NXQWGHSXQWHQGHNRPPDPHWHONDDUYHUZLVVHOHQDOV

GHFLPDDOVFKHLGLQJVWHNHQRIDOVVFKHLGLQJVWHNHQWXVVHQ

FLMIHUV$QJHOVDNVLVFKHYHUVXVLQWHUQDWLRQDOHQRWDWLHGRRU

RS

WHGUXNNHQ

(pQPLOMRHQNDQELMYRRUEHHOGDOVZRUGHQ

JHWRRQGRIDOV

Toetsen: Display: Beschrijving:

1,43

9RHUWGHGHOLQJXLW

142857142857

7RRQWDOOHFLMIHUV

10B.book Page 31 Wednesday, June 28, 2000 3:31 PM

32 1: Om te beginnen

Het afronden van getallen

'HFDOFXODWRUVODDWJHWDOOHQRSLQ FLMIHUVHQUHNHQW

HYHQHHQVPHWJHWDOOHQYDQFLMIHUV$OVGH

QDXZNHXULJKHLGYDQFLMIHUVQLHWZHQVHOLMNLVNXQWXPHW

KHWJHWDODIURQGHQQDDUGHQ RWDWLHYDQGHGLVSOD\

YRRUGDWXKHWYRRUHHQYHUGHUHEHUHNHQLQJJHEUXLNW+HW

DIURQGHQYDQFLMIHUVLV]HHUKDQ GLJDOVXGHZHUNHOLMNH

PDDQGHOLMNHEHWDOLQJHQGROODUVHQFH QWVZLOWEHUHNHQHQ

Meldingen

'H+3%,,JHHIWPHOGLQJHQZHHURYHUGHVWDWXVYDQGHFDOFXODWRUZHHU

RIODDWXZHWHQZDQQHHUXHHQYHUNHHUGHEHZHUNLQJSUREHHUWXLWWH

YRHUHQ'RRURS

RI WHGUXNNHQYHUZLMGHUWXGHPHOGLQJYDQGH

GLVSOD\=LH´0HOGLQJHQµRSSDJLQD YRRUHHQYHUNODULQJYDQGH

PHOGLQJHQ

Toetsen: Display: Beschrijving:

9,87654321_

9RHUWHHQJHWDOLQPHW

PHHUGDQWZHHGHFL

PDOHQYHUVFKLOOHQGYDQ

QXO

9,88

7RRQWWZHHGHFLPDOHQ

987654321000

7RRQWDOOHFLMIHUV

]RQGHUGHGHFLPDOH

SXQW]RODQJX

LQJH

GUXNWKRXGW

9,88

5RQGWDIRSWZHHGHFL

PDOHQLQJHVWHOGGRRU

KHWLQWRHWVHQYDQ

KLHUYRRU

988000000000

7RRQWKHWDIJHURQGHHQ

RSJHVODJHQJHWDO

10B.book Page 32 Wednesday, June 28, 2000 3:31 PM

2: Economische percentages 33

Economische percentages

8NXQWGH+3%,,JHEUXLNHQRPSHUFHQWDJHVSURFHQWXHOH

YHUDQGHULQJHQNRVWHQSULMVPDUJHHQEUXWRZLQVWWHEHUHNHQHQ

Procenttoets

'H WRHWVKHHIWWZHHIXQFWLHVKHWEHUHNHQHQYDQHHQ

SHUFHQWDJHHQKHWRSWHOOHQRIDIWUHNNHQYDQHHQ

SHUFHQWDJH

Een percentage berekenen

'H WRHWVGHHOWHHQJHWDOGRRUWHQ ]LMHUHHQSOXVRIHHQPLQWHNHQ

DDQYRRUDIJDDW

Voorbeeld. %HUHNHQYDQ

Toetsen: Display: Beschrijving:

200,00

9RHUWLQ

0,25

=HWRPLQHHQGHFL

PDDOJHWDO

50,00

9HUPHQLJYXOGLJWPHW



10B.book Page 33 Wednesday, June 28, 2000 3:31 PM

34 2: Economische percentages

Een percentage optellen of aftrekken

8NXQWLQppQEHUHNHQLQJHHQSHUF HQWDJHRSWHOOHQRI DIWUHNNHQ

Voorbeeld. 9HUPLQGHUPHW

Voorbeeld. 8OHHQWYDQHHQYULHQ GHQXNRPWRYHUHHQRPGH

OHQLQJQDppQMDDUPHWHQNHOYRXGLJHUHQWHWHUXJWHEHWDOHQ:DWEHQWX

GDQVFKXOGLJ"

Procentuele verandering

%HUHNHQWGHSURFHQWXHOHYHUDQGHULQJWXVVH QWZHHJHWDOOHQ

Q

HQQ  XLWJHGUXNWDOVSHUFHQWDJHYDQQ GRRUQ Q 

LQWHYRHUHQHQYHUYROJHQVRS

WHGUXNNHQ

Voorbeeld. %HUHNHQGHSURFHQ WXHOHYHUDQGHULQJWXVVHQ

HQ

Toetsen: Display: Beschrijving:

200,00

9RHUWLQ

50,00

9HUPHQLJYXOGLJW

PHW

150,00

7UHNWYDQDI

Toetsen: Display: Beschrijving:

87,50

%HUHNHQWGHUHQWHYDQ

GHOHQLQJ

1.337,50

7HOWHQ

ELMHONDDURSHQWRRQW

EHGUDJGDWXPRHWWHU

XJEHWDOHQ

Toetsen: Display: Beschrijving:

291,70

9RHUWQ LQ

8,60

%HUHNHQWGHSURFHQWX

HOHYHUDQGHULQJ

10B.book Page 34 Wednesday, June 28, 2000 3:31 PM

2: Economische percentages 35

Voorbeeld. %HUHNHQGHSURFHQ WXHOHYHUDQGHULQJWXVVHQïHQ



Berekening van marge en brutowinst

'H+3%,,NDQNRVWHQYHUNRRSSULMVPDUJHRIEUXWRZLQVWEHUHNHQHQ

$OVXHHQYDQGHZDDUGHQZLOWEHNLMNHQGLHELMGHEHUHNHQLQJYDQPDUJH

HQEUXWRZLQVWZRUGWJHEUXLNWGUXNWXRS

HQYHUYROJHQVRSGHWRHWV

GLHXZLOWEHNLMNHQ%LMYRRUEHHOGDOVXGHZDDUGHGLHLQ

LVRSJHVODJHQ

ZLOW]LHQGUXNWXRS

0DUJHHQEUXWRZLQVWKHEEHQKHW]HOIGH

RSVODJUHJLVWHU$OVXRSVODDWLQ

HQYHUYROJHQ VRS GUXNW]LHW

X

Margeberekeningen

Voorbeeld. .LORZDWW(OHFWURQLFVNRRSWWHOHYLVLHVLQYRRU'H

WHOHYLVLHVZRUGHQWHJHQYHUNRFKW+RHJURRWLVGHPDUJH"

Toetsen: Display: Beschrijving:

60,00

%HUHNHQWHQYRHUWQ LQ

38,33

%HUHNHQWSURFHQWXHOH

YHUDQGHULQJ

Toepassing Toetsen Beschrijving

0DUJH

, ,

'HPDUJHLVGHEUXWRZLQVWXLW

JHGUXNWDOVSHUFHQWDJHYDQGH

SULMV

%UXWRZLQVW

, ,

%UXWRZLQVWEHUHNHQLQJHQ

ZRUGHQXLWJHGUXNWDOVSHUFHQW

DJHYDQGHNRVWHQ

Toetsen: Display: Beschrijving:

255,00

6ODDWGHNRVWHQLQN

RRSSULMVRSLQ&67

300,00

6ODDWGHYHUNRRSSULMV

RSLQ35&

15,00

%HUHNHQWGHPDUJH

10B.book Page 35 Wednesday, June 28, 2000 3:31 PM

36 2: Economische percentages

Berekeningen van de brutowinst ten opzichte van de

kosten

Voorbeeld. 'HVWDQGDDUGE UXWRZLQVWRSNHWWLQJHQLVELM.OHLQ HU·V

.RVPHWLTXH=LMKHEEHQHHQ]HQGLQJFKRNHUFROOLHUVR QWYDQJHQGLH

SHUVWXNNRVWHQ:DWLVGHYHUNRRSSULMVSHUFKRNHU"

Marge en brutowinst tegelijkertijd gebruiken

Voorbeeld. (HQFR|SHUDWLHILQNRRSEXUHD XNRRSWNLVWHQPHWEOLNNHQ

VRHSLQWHJHQHHQ IDFWXXUSULMVYDQSHUNLVW$OVGHFR| SHUDWLH

JHZRRQOLMNHHQ EUXWRZLQVWYDQKDQWHHUWWHJHQZHONHSULMVPRHWHHQ

NLVWVRHSEOLNNHQGDQZRUGHQYHUNRFKW"(QKRHJURRWLVGHPDUJH"

Toetsen: Display: Beschrijving:

19,00

6ODDWGHNRVWHQRS

60,00

6ODDWGHEUXWRZLQVWRS

30,40

%HUHNHQWGHYHUNRRS

SULMV

Toetsen: Display: Beschrijving:

9,60

6ODDWGHLQNRRSNRVWHQ

RS

15,00

6ODDWGHEUXWRZLQVWRS

11,04

%HUHNHQWGHSULMVYDQ

HHQNLVWVRHSEOLNNHQ

13,04

%HUHNHQWGHPDUJH

10B.book Page 36 Wednesday, June 28, 2000 3:31 PM

3: Het opslaan van getallen en rekenkundige bewerkingen 37

Het opslaan van getallen en

rekenkundige bewerkingen

Het gebruik van opgeslagen getallen bij

berekeningen

8NXQWRSYHUVFKLOOHQGHPDQLHUHQJHWDOOHQRSVODDQHQGH]HYHUYROJHQV

RSQLHXZJHEUXLNHQ

*HEUXLN FRQVWDQWRPHHQJHWDOHQGHGDDUELMEHKRUHQGH

RSHUDQGRSWHVODDQDOVXGLWYDDNZLOWJHEUXLNHQ

*HEUXLNJHKHXJHQWRHWVHQ  HQ RPPHWppQ

WRHWVDDQVODJJHWDOOHQRSWHVODDQWHODGHQHQELMHONDDURSWHWHOOHQ

*HEUXLN HQ RPJHWDOOHQRSWHVODDQLQRIWHODGHQXLWGH

JHQXPPHUGHUHJLVWHUV

Het gebruik van constanten

*HEUXLN RPHHQJHWDOHQHHQUHNHQNXQGLJHRSHUDWRU

RSWHVODDQYRRUKHUKDOHQGHEHZHUNLQJHQ1DGDWGH

FRQVWDQWHEHZHUNLQJLVRSJHVODJHQYRHUWXHHQJHWDOLQHQ

GUXNWXRS

'HRSJHVODJHQEHZHUNLQJZRUGWXLWJHYRHUG

PHWKHWJHWDOGDWLQGHGLVSOD\VWDDW

10B.book Page 37 Wednesday, June 28, 2000 3:31 PM

38 3: Het opslaan van getallen en rekenkundige bewerkingen

Voorbeeld. %HUHNHQHQ

Voorbeeld. %HUHNHQHQ

Toetsen Bewerking

JHWDO

6ODDW´JHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´²JHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´ïJHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´¸JHWDOµRSDOVHHQFRQVWDQWH

[ZDDUGH

6ODDW´\ µRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´JHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´²JHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´ïJHWDOµRSDOVHHQFRQVWDQWH

JHWDO

6ODDW´¸JHWDOµRSDOVHHQFRQVWDQWH

Toetsen: Display: Beschrijving:

2,00

6ODDW´µRSDOVHHQ

FRQVWDQWH

7,00

7HOWRS

8,00

7HOWRS

9,00

7HOWRS

Toetsen: Display: Beschrijving:

1,00

6ODDW´µRSDOV

HHQFRQVWDQWH

11,00

7HOWELMRS

12,10

7HOWELMRS

27,50

7HOWELMRS

10B.book Page 38 Wednesday, June 28, 2000 3:31 PM

3: Het opslaan van getallen en rekenkundige bewerkingen 39

Voorbeeld. %HUHNHQ HQ 

Het gebruik van het M-register

'H  HQ WRHWVHQYRHUHQJHKHXJHQEHZHUNLQJHQ

XLWRSHHQHQNHOYRXGLJRSVODJUHJLVWHUKHW0UHJLVWHU,QGH

PHHVWHJHYDOOHQLVKHWQLHWQRGLJRPKHW0UHJLVWHUWH

ZLVVHQDDQJH]LHQPHW

GHUHHGVDDQZH]LJHLQKRXG

ZRUGWYHUYDQJHQ8NXQWKHW0UHJLVWHUHFKWHUZLVVHQ

GRRURS

 WHGUXNNHQ$OVXHHQDDQWDOJHWDOOHQDDQ

KHW0UHJLVWHUWRHYRHJWNXQWX

JHEUXLNHQRPKHW

HHUVWHJHWDORSWHVODDQHQ

RPGHYROJHQGHJHWDOOHQLQWHEUHQJHQ8

WUHNWKHWZHHUJHJHYHQJHWDOYDQKHWJHWDOLQKHW0UHJLVWHUDIGRRURS



HQYHUYROJHQVRS

WHGUXNNHQ

Voorbeeld. 7HOPHWEHKXOSYDQKHW0UHJLVWHUDQGELM

HONDDURS7UHNGDDUYHUYROJHQVYDQDIHQKDDOKHWUHVXOWDDWRS

Toetsen: Display: Beschrijving:

3,00

6ODDW´\ µRSDOVHHQFRQVWDQWH

8,00

%HUHNHQW 

64,00

%HUHNHQW 

Toetsen Beschrijving

6ODDWKHWZHHUJHJHYHQJHWDOLQKHW0UHJLVWHURS

+DDOWKHWJHWDOXLWKHW0UHJLVWHURS

7HOWKHWZHHUJHJHYHQJHWDORSELMKHWLQJHWDOLQ

KHW0UHJLVWHU

Toetsen: Display: Beschrijving:

17,00

6ODDWLQKHW0UHJLVWHURS

14,25

7HOWELMKHW0UHJLVWHURS

16,95

7HOWELMKHW0UHJLVWHURS

–4,65

7HOW²ELMKHW0UHJLVWHURS

43,55

+DDOWGHLQKRXGYDQKHW0

UHJLVWHURS

10B.book Page 39 Wednesday, June 28, 2000 3:31 PM

40 3: Het opslaan van getallen en rekenkundige bewerkingen

Het gebruik van genummerde registers

0HWGH HQ WRHWVHQNULMJWXWRHJDQJWRWGH

RSVODJUHJLVWHUV0HWGH

WRHWVNRSLHHUWXKHW

ZHHUJHJHYHQJHWDOQDDUHHQEHSDDOGUHJLVWHU0HWGH



WRHWVNRSLHHUWXHHQJHWDOXLWHHQUHJLVWHUQDDUGHGLVSOD\

(HQJHWDORSVODDQRIRSYUDJHQLQWZHHVWDSSHQ

 'UXNRS

RI $OVXGH]HVWDSRQJHGDDQZLOWPDNHQGUXNW

XRS

RIRS 

 9RHUKHWQXPPHUYDQKHWUHJLVWHULQWRWHQPHW

,QKHWYROJHQGHYRRUEHHOGZRUGHQWZHHRSVODJUHJLVWHUVJHEUXLNW

%HUHNHQKHWYROJHQGH

HQ

8NXQW

HQ RRNJHEUXLNHQYRRUWRHSDVVLQJVUHJLVWHUVPDDUQLHW

ELMVWDWLVWLHN%LMYRRUEHHOGPHW

VODDWXKHWJHWDOGDWLQGH

GLVSOD\VWDDWLQKHW

UHJLVWHURS0HW NRSLHHUWXGHLQKRXGYDQ

QDDUGHGLVSOD\

,QGHPHHVWHJHYDOOHQLVKHWQLHWQRGLJRPGHRSVODJUHJLVWHUVWHZLVVHQ

RPGDWGRRUKHWRSVODDQYDQJHWDOOHQGHUHHGVDDQZH]LJHLQKRXGZRUGW

YHUYDQJHQ8NXQWDI]RQGHUOLMNHUHJLVWHUVZLVVHQGRRUHULQRSWHVODDQ

8ZLVWDOOHUHJLVWHUVWHJHOLMNHUWLMGGRRURS

WHGUXNNHQ

Toetsen: Display: Beschrijving:

475,60

6ODDWKHWZHHUJHJHYHQ

JHWDOLQ5

RS

39,15

6ODDWLQ5 RS

12,15

+LHUPHHLVGHHHUVWHEHUHNHQLQJ

DI

475,60

9UDDJW5 RS

39,15

9UDDJW5 RS

26,45

+LHUPHHLVGHWZHHGH

EHUHNHQLQJDI

475

39 15,

---------------

560

, 475

15,

-------------------------------------

10B.book Page 40 Wednesday, June 28, 2000 3:31 PM

3: Het opslaan van getallen en rekenkundige bewerkingen 41

Rekenkundige bewerkingen uitvoeren binnen een

8NXQWLQGHRSVODJUHJLVWHUV5 WRWHQPHW5 UHNHQNXQGLJHEHZHUNLQJHQ

XLWYRHUHQ+HWUHVXOWDDWZRUGWLQKHWUHJLVWHURSJHVODJHQ

Voorbeeld. 6ODLQ5 RSYHUPHQLJYXOGLJGLWPHWHQVODKHW

UHVXOWDDWLQ5

RS

Toetsen Nieuw getal in register

UHJLVWHUQXPPHU 5HHGVDDQZH]LJHLQKRXGKHW

ZHHUJHJHYHQJHWDO

UHJLVWHUQXPPHU 5HHGVDDQZH]LJHLQKRXG²KHW

ZHHUJHJHYHQJHWDO

UHJLVWHUQXPPHU 5HHGVDDQZH]LJHLQKRXGïKHW

ZHHUJHJHYHQJHWDO

UHJLVWHUQXPPHU 5HHGVDDQZH]LJHLQKRXG¸KHW

ZHHUJHJHYHQJHWDO

Toetsen: Display: Beschrijving:

45,70

6ODDWLQ5 RS

2,50

9HUPHQLJYXOGLJW

LQ5

PHWHQVODDW

KHWUHVXOWDDWLQ

RS

114,25

*HHIW5 ZHHU

10B.book Page 41 Wednesday, June 28, 2000 3:31 PM

42 3: Het opslaan van getallen en rekenkundige bewerkingen

Rekenkundige bewerkingen uitvoeren

:LVNXQGLJHIXQFWLHVZRUGHQRSKHWJHWDOLQGHGLVSOD\

XLWJHYRHUG

Voorbeeld. %HUHNHQ  HQYHUYROJHQV  

Voorbeeld. %HUHNHQGHQDWXXUOLMNHORJDULWPHH %HUHNHQYHUYROJHQV



Toetsen: Display: Beschrijving:

0,25

%HUHNHQWGHUHFLSURTXH

YDQ

4,47

%HUHNHQW

√



51,67

%HUHNHQW

√



1,21

%HUHNHQW 

52,88

'HEHZHUNLQJLVNODDU

Toetsen: Display: Beschrijving:

12,18

%HUHNHQWH 

2,50

%HUHNHQWGHQDW

XXUOLMNHORJDULWPHYDQ

KHWUHVXOWDDW

24,00

%HUHNHQWIDFXOWHLW

814,00

'HEHZHUNLQJLVNODDU



10B.book Page 42 Wednesday, June 28, 2000 3:31 PM

3: Het opslaan van getallen en rekenkundige bewerkingen 43

Machtverheffingsoperator

'HPDFKWYHUKHIILQJVRSHUDWRU YHUKHIWKHW

YRRUJDDQGHJHWDO\ZDDUGHWRWGHPDFKWYDQKHW

GDDURSYROJHQGHJHWDO[ZDDUGH

Voorbeeld. %HUHNHQ HQEHUHNHQYHUYROJHQVGHGHUGHPDFKWVZRUWHO

YDQ

Het gebruik van haakjes in berekeningen

'RRUKDDNMHVWHJHEUXLNHQNXQWXKHWEHUHNHQHQYDQHHQWXVVHQWLMGV

UHVXOWDDWXLWVWHOOHQWRWGDWXPHHUJHWDOOHQKHEWLQJHYRHUG8NXQWWRWYLHU

RSHQKDDNMHVJHEUXLNHQLQHONHEHUHNHQLQJ9HURQGHUVWHOGDWXKHW

YROJHQGHZLOWEHUHNHQHQ

$OVX

LQYRHUWJHHIWGHFDOFXODWRUKHWWXVVHQWLMGVUHVXOWDDW

ZHHU'LWUHVXOWDDWNULMJWXRPGDWEHUHNHQLQJHQZDDUJHHQKDDNMHVLQ

VWDDQYDQOLQNVQDDUUHFKWVZRUGHQXLWJHYRHUGQHW]RDOVX]HLQYRHUW$OV

XGHGHOLQJZLOWXLWVWHOOHQWRWGDWXYDQKHEWDIJHWURNNHQPRHWX

KDDNMHVJHEUXLNHQ+HWVOXLWHQYDQGHKDDNMHVDDQKHWHLQGHYDQHHQ

XLWGUXNNLQJNDQZRUGHQZHJJHODWHQ%LMYRRUEHHOGKHWLQYRHUHQYDQ´

ï µLVJHOLMNDDQKHWLQYRHUHQYDQ´

ï µ

Toetsen: Display: Beschrijving:

1.953.125,00

%HUHNHQW 

5,00

%HUHNHQWGHGHUGH

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10B.book Page 43 Wednesday, June 28, 2000 3:31 PM

44 3: Het opslaan van getallen en rekenkundige bewerkingen

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10B.book Page 44 Wednesday, June 28, 2000 3:31 PM

4: Financiële problemen in beeld brengen 45

Financiële problemen in beeld

brengen

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10B.book Page 45 Wednesday, June 28, 2000 3:31 PM

46 4: Financiële problemen in beeld brengen

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10B.book Page 46 Wednesday, June 28, 2000 3:31 PM

4: Financiële problemen in beeld brengen 47

Periodes en cashflows

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10B.book Page 47 Wednesday, June 28, 2000 3:31 PM

48 4: Financiële problemen in beeld brengen

Samengestelde rente

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10B.book Page 48 Wednesday, June 28, 2000 3:31 PM

4: Financiële problemen in beeld brengen 49

De rentevoet

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10B.book Page 49 Wednesday, June 28, 2000 3:31 PM

50 4: Financiële problemen in beeld brengen

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GH]HOIGHJURRWWHZRUGHQJHZRRQOLMNDOV790YUDDJVWXNNHQEHKDQGHOG

+LHURQGHUYLQGWXHHQFDVKIORZGLDJUDPYDQHHQNUHGLHWQHPHUYRRUHHQ

MDULJHK\SRWKHHNYDQPHWEHWDOLQJHQYDQWHJHQ

MDDUOLMNVHUHQWHPHWHHQDIEHWDOLQJYDQYDQGHKRRIGVRP

EDOORQEHWDOLQJ

(pQYDQGHZDDUGHQYDQ39307)9

NDQJHOLMNDDQQXO]LMQ+LHURQGHU

]LHWXHHQFDVKIORZGLDJUDPYDQXLWKHWVWDQGSXQWYDQGHVSDDUGHUYRRU

HHQVSDDUUHNHQLQJPHWHHQHHQPDOLJGHSRVLWRHQHHQHHQPDOLJHRSQDPH

YLMIMDDUODWHU'HUHQWHZRUGWPDDQGHOLMNVVDPHQJHVWHOG,QGLWYRRUEHHOG

LV307

JHOLMNDDQQXO

$DQWDOSHULRGHVRIEHWDOLQJHQ

-DDUOLMNVHUHQWHYRHWJHZRRQOLMNGHMDDUOLMNVHQRPLQDOHUHQWH

+XLGLJHZDDUGHGHFDVKIORZDDQKHWEHJLQYDQGHWLMGOLMQ

3HULRGLHNHEHWDOLQJ

7RHNRPVWLJHZDDUGHGHFDVKIORZDDQKHWHLQGYDQKHWFDVKIORZ

GLDJUDPRSJHWHOGELMSHULRGLHNHEHWDOLQJHQ

10B.book Page 50 Wednesday, June 28, 2000 3:31 PM

4: Financiële problemen in beeld brengen 51

790EHUHNHQLQJHQZRUGHQLQKHWYROJHQGHKRRIGVWXNEHKDQGHOG

Het herkennen van een cashflowvraagstuk

(HQILQDQFLHHOYUDDJVWXNZDDUELMJHHQVSUDNHLVYDQUHJHOPDWLJH

XQLIRUPHEHWDOLQJHQVRPVRQHYHQFDVKIORZVJHQRHPGLVHHQ

FDVKIORZYUDDJVWXNHQJHHQ790YUDDJVWXN

+LHURQGHUYLQGWXHHQFDVKIORZGLDJUDPYRRUHHQLQYHVWHULQJLQHHQ

EHOHJJLQJVIRQGV'LWLVHHQYRRUEHHOGYDQHHQYUDDJVWXNGDWRIPHW

QHWWRKXLGLJHZDDUGHRIPHW LQWHUQMDDUOLMNVUHQGHPHQW

ZRUGWRSJHORV

10B.book Page 51 Wednesday, June 28, 2000 3:31 PM

52 4: Financiële problemen in beeld brengen

&DVKIORZYUDDJVWXNNHQZRUGHQEHVFKUHYHQLQKRRIGVWXN

10B.book Page 52 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 53

“Time Value of Money”-

berekeningen

Het gebruik van de TVM-functie

'H790IXQFWLHZRUGWJHEUXLNWELMGHEHUHNHQLQJYDQ

VDPHQJHVWHOGHUHQWHZDDUELMVSUDNHLVYDQXQLIRUPH

FDVKIORZVGLHZHEHWDOLQJHQQRHPHQ1DGDWGHZDDUGHQ

]LMQLQJHYRHUGNXQWXWHONHQVppQZDDUGHYDULsUHQ]RQGHU

DOOHZDDUGHQRSQLHXZLQWHYRHUHQ

(UPRHWDDQEHSDDOGHYRRUZDDUGHQZRUGHQYROGDDQRPGH790IXQFWLH

WHNXQQHQJHEUXLNHQ

+HWEHGUDJYDQLHGHUHEHWDOLQJPRHWJHOLMN]LMQ$OVGHJURRWWHYDQGH

EHWDOLQJHQYDULHHUWPRHWXGHZHUNZLM]HYROJHQGLHEHVFKUHYHQVWDDW

LQKRRIGVWXN´&DVKIORZEHUHNHQLQJHQµ

%HWDOLQJHQPRHWHQPHWUHJHOPDWLJHWXVVHQSR]HQJHGDDQZRUGHQ

'HEHWDOLQJVSHULRGHPRHWVDPHQYDOOHQPHWGHSHULRGHZDDURYHUGH

VDPHQJHVWHOGHUHQWHZRUGWEHUHNHQG,VGLWQLHWKHWJHYDOYHUDQGHU

GDQGHUHQWHYRHWPHWGHWRHWVHQ

 HQ ]RDOVGDW

RSSDJLQD ZRUGWEHVFKUHYHQ

(UPRHWWHQPLQVWHppQSRVLWLHYHHQppQQHJDWLHYHFDVKIORZ

YRRUNRPHQ

10B.book Page 53 Wednesday, June 28, 2000 3:31 PM

54 5: “Time Value of Money”-berekeningen

8NXQWZDDUGHQYHULILsUHQGRRURS    HQ

WHGUXNNHQ$OVXRS GUXNWZRUGWKHWWRWDDODDQWDO

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GUXNW

ZRUGWKHWDDQWDOEHWDOLQJHQSHUMDDURSJHURHSHQ+HWRSYUDJHQYDQGH]H

JHWDOOHQYHUDQGHUWGHLQKRXGYDQGHUHJLVWHUVQLHW

Toets Slaat op of berekent

+HWDDQWDOEHWDOLQJHQRIFXPXODWLHYHSHULRGHV

'HMDDUOLMNVHQRPLQDOHUHQWHYRHW

'HKXLGLJHZDDUGHYDQWRHNRPVWLJHFDVKIORZV39

LVJHZRRQOLMNHHQHHUVWHLQYHVWHULQJRIHHQJHOHHQG

EHGUDJHQNRPWDOWLMGDDQKHWEHJLQYDQGHHHUVWH

SHULRGHYRRU

+HWEHGUDJYDQGHSHULRGLHNHEHWDOLQJHQ$OOH

EHWDOLQJHQ]LMQHYHQJURRWHQHUZRUGWJHHQHQNHOH

RYHUJHVODJHQEHWDOLQJHQNXQQHQDDQKHWEHJLQRI

DDQKHWHLQGYDQGHSHULRGHJHGDDQZRUGHQ

'HWRHNRPVWLJHZDDUGH)9LVRIHHQODDWVWHFDVK

IORZRIGHVDPHQJHVWHOGHZDDUGHYDQHHQUHHNVHHU

GHUHFDVKIORZV)9NRPWDDQKHWHLQGYDQGH

ODDWVWHSHULRGHYRRU

6ODDWKHWDDQWDOSHULRGHVSHUMDDURS'HVWDQGDDUG

ZDDUGHLV6WHOGLWDOOHHQRSQLHXZLQDOVXHHQ

YHUDQGHULQJZLOWDDQEUHQJHQ'H]HWRHWVEHYLQGW

]LFKRQGHUGH

WRHWV

2SWLRQHOHYHUNRUWHPDQLHUYRRUKHWLQYRHUHQYDQ

1KHWJHWDOLQGHGLVSOD\ZRUGWYHUPHQLJYXOGLJG

PHWGHZDDUGHLQ3<5HQKHWUHVXOWDDWZRUGWLQ1

RSJHVODJHQ'H]HWRHWVYLQGWXRQGHUGH

WRHWV

:LVVHOWWXVVHQGH%HJLQHQ(LQGPRGXV,QGH

%HJLQPRGXV]LHWXGH

BEGINLQGLFDWRU

%HUHNHQWHHQDIEHWDOLQJVWDEHO

10B.book Page 54 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 55

TVM-registers wissen

'RRURS WHGUXNNHQZLVWXDOOH790UHJLVWHUV+LHUGRRUNULMJHQ

1,<539307HQ)9GHZDDUGHQXO'HKXLGLJHZDDUGHYDQ3<5

YHUVFKLMQWNRUWLQGHGLVSOD\

Begin- en Eindmodus

9RRUGDWXDDQHHQ790EHUHNHQLQJEHJLQWPRHWX

DDQJHYHQRIGHHHUVWHSHULRGLHNHEHWDOLQJDDQKHWEHJLQRI

DDQKHWHLQGYDQGHHHUVWHSHULRGHYRRUNRPW$OVGHHHUVWH

EHWDOLQJDDQKHWHLQGYDQGHHHUVWHSHULRGHJHEHXUWPRHW

XGH+3%,,RS(LQGPRGXVLQVWHOOHQ$OVGH]HDDQKHW

EHJLQYDQGHHHUVWHSHULRGHYRRUNRPWGDQVWHOWXGH

FDOFXODWRURSGH%HJLQPRGXVLQ

8NXQWWXVVHQ%HJLQHQ(LQGPRGXVRPVFKDNHOHQGRRURS

WH

GUXNNHQ$OVGHFDOFXODWRULQGH%HJLQPRGXVLV]LHWXGH

BEGIN

LQGLFDWRU8]LHWJHHQLQGLFDWRUDOVXLQGH(LQGPRGXVEHQW

+\SRWKHNHQHQOHQLQJHQJHEUXLNHQPHHVWDOGH(LQGPRGXV

/HDVHFRQWUDFWHQHQVSDDUSODQQHQJHEUXLNHQRYHUKHWDOJHPHHQGH

%HJLQPRGXV

Het berekenen van leningen

Voorbeeld: Een autolening. 8ILQDQFLHUWHHQDXWRPHWHHQOHQLQJYDQ

GULHMDDUWHJHQMDDUOLMNVHQRPLQDOHUHQWHPDDQGHOLMNVVDPHQJHVWHOG

'HDXWRNRVW8EHWDDOWYRRUXLW

Deel 1. :DW]LMQXZPDDQGHOLMNVHEHWDOLQJHQELMHHQUHQWHYDQ"

1HHPDDQGDWXHHQPDDQGQDGHDDQNRRSRIDDQKHWHLQGYDQGHHHUVWH

SHULRGHEHJLQWPHWGHDIEHWDOLQJHQ

10B.book Page 55 Wednesday, June 28, 2000 3:31 PM

56 5: “Time Value of Money”-berekeningen

6WHOGH(LQGPRGXVLQ'UXNRS DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOSHUL

RGHVSHUMDDULQ

36,00

6ODDWKHWDDQWDO

SHULRGHVYDQGHOHQLQJ

RS

10,50

6ODDWGHMDDUOLMNVH

QRPLQDOHUHQWHYRHWRS

13.000,00

6ODDWKHWJHOHHQGH

EHGUDJRS

0,00

6ODDWKHWEHGUDJRSGDW

QRJXLWVWDDWQDGULHMDDU

–422,53

%HUHNHQWGHPDDQ

GHOLMNVHDIEHWDOLQJ+HW

PLQWHNHQJHHIWKHW

EHWDDOGHEHGUDJDDQ

10B.book Page 56 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 57

Deel 2. %LMZHONHUHQWHYRHWZRUGWKHWPDDQGHOLMNVWHEHWDOHQEHGUDJPHW

YHUPLQGHUGWRWELMHHQKRRIGVRPYDQ"

Deel 3. $OVGHUHQWHLVHQXSHUPDDQGQLHWPHHUGDQZLOW

EHWDOHQZDWNXQWXGDQPD[LPDDODDQHHQQLHXZHDXWRXLWJHYHQ"

Voorbeeld: Een hypotheek op een huis. 8YLQGWGDWKHWPD[LPDOH

PDDQGHOLMNVHEHGUDJGDWXDDQHHQK\SRWKHHNNXQWXLWJHYHQLV8

NXQWHHQYRRUXLWEHWDOLQJPDNHQYDQHQGHMDDUOLMNVHUHQWHYRHWLV

RSKHWRJHQEOLN$OVXHHQK\SRWKHHNYRRUMDDUNXQWNULMJHQZDW

LVGDQGHPD[LPDOHDDQNRRSSULMVGLHX]LFKNXQWYHURRUORYHQ"

–372,53

9HUPLQGHUWGHEHWDOLQJ

WRYGHHHUGHUEHUHN

HQGH

2,03

%HUHNHQWGHMDDUOLMNVH

UHQWHYRHWYRRUGH

JHUHGXFHHUGHEHWDOLQJ

10,50

6ODDWGHRRU

VSURQNHOLMNHUHQWHYRHW

RS

–375,00

6ODDWGHJHZHQVWH

EHWDOLQJRS

11.537,59

%HUHNHQWKHWWHILQDQ

FLHUHQEHGUDJ

13.037,59

7HOWGHYRRUXLWEHWDOLQJ

RSELMKHWJHILQDQFLHUGH

EHGUDJRPGHWRWDOH

SULMVYDQGHDXWRWHNULM

JHQ

10B.book Page 57 Wednesday, June 28, 2000 3:31 PM

58 5: “Time Value of Money”-berekeningen

6WHOGH(LQGPRGXVLQ'UXNRS DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOSHUL

RGHVSHUMDDULQ

360,00

6WHOWGHGXXUYDQGH

K\SRWKHHNLQï

0,00

%HWDDOWGHK\SRWKHHNLQ

MDDUDI

7,50

6ODDWGHUHQWHYRHWRS

–930,00

6ODDWGHJHZHQVWH

EHWDOLQJRSXLWEH

WDDOGHEHGUDJLV

QHJDWLHI

133.006,39

%HUHNHQWKRHJURRWGH

OHQLQJLVELMPDDQ

GHOLMNVHEHWDOLQJHQYDQ



145.006,39

7HOWDDQ

YRRUXLWEHWDOLQJRSRP

GHWRWDOHDDQNRRSSULMV

WHNULMJHQ

10B.book Page 58 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 59

Voorbeeld: Een hypotheek met een ballonbetaling. 8KHEWHHQ

K\SRWKHHNYDQJHNUHJHQYRRUMDDUWHJHQHHQMDDUOLMNVH

UHQWHYRHWYDQ8YRRU]LHWGDWXKHWKXLVQDYLHUMDDU]XOWYHUNRSHQ

HQGHOHQLQJPHWHHQEDOORQEHWDOLQJ]XOWWHUXJEHWDOHQ:DW]DOGH

EDOORQEHWDOLQJ]LMQ"

/RVGLWSUREOHHPRSLQWZHHHWDSSHV

 %HUHNHQGHEHWDOLQJRSGHOHQLQJRSEDVLVYDQHHQWHUPLMQYDQ

MDDU

 %HUHNHQKHWRYHUEOLMYHQGHVDOGRQDYLHUMDDU

Punt 1. %HUHNHQHHUVWGHEHWDOLQJRSGHOHQLQJJHEDVHHUGRSHHQWHUPLMQ

YDQMDDU

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOSHULRGHVSHUMDDU

LQ

300,00

6ODDWGHGXXUYDQGHK\SRWKHHN

RSï PDDQGHQ

0,00

6ODDWKHWVDOGRYDQGHOHQLQJQD

MDDURS

172.500,00

6ODDWKHWVDOGRYDQGH

RRUVSURQNHOLMNHOHQLQJRS

8,80

6ODDWGHMDDUOLMNVHUHQWHYRHWRS

–1.424,06

%HUHNHQWGHPDDQGHOLMNVH

DIEHWDOLQJ

10B.book Page 59 Wednesday, June 28, 2000 3:31 PM

60 5: “Time Value of Money”-berekeningen

Punt 2. $DQJH]LHQGHEHWDOLQJDDQKHWHLQGYDQGHPDDQGZRUGWJHGDDQ

ZRUGHQGHODDWVWHEHWDOLQJHQGHEDOORQEHWDOLQJWHJHOLMNHUWLMGJHGDDQ'H

ODDWVWHEHWDOLQJLVGHVRPYDQ307HQ)9

'HZDDUGHLQ307PRHWELMKHWEHUHNHQHQYDQ)9RI39

DOWLMGRSWZHHGHFLPDOHQDIJHURQGZRUGHQRPNOHLQH]LFK

FXPXOHUHQGHYHUVFKLOOHQWXVVHQQLHWDIJHURQGHHQ

ZHUNHOLMNHGROODUVHQFHQWVEHWDOLQJHQWHYHUPLMGHQ$OV

GHGLVSOD\QLHWRSWZHHGHFLPDOHQLVLQJHVWHOGGUXNWXRS



Toetsen: Display: Beschrijving:

–1.424,06

5RQGWEHWDOLQJHQRSWZHH

GHFLPDOHQDIHQVODDWGH]H

GDQRS

48,00

6ODDWGHWHUPLMQYDQYLHUMDDU

ïGLHXYHUZDFKWKHW

KXLVWHEH]LWWHQRS

–163.388,39

%HUHNHQWKHWVDOGRYDQGH

OHQLQJQDYLHUMDDU

–164.812,45

%HUHNHQWKHWWRWDDOYDQGH 

EHWDOLQJ307HQ)9YRRU

KHWDIORVVHQYDQGHOHQLQJ

KHWWHEHWDOHQEHGUDJZRUGW

DDQJHGXLGDOVHHQQHJDWLHI

JHWDO

10B.book Page 60 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 61

Berekeningen met spaarsystemen

Voorbeeld: Een spaarrekening. $OVXRSHHQVSDDUUHNHQLQJ

VWRUWZDDUXHHQMDDUOLMNVHUHQWHYRHWYDQNULMJWHQYHUGHUJHHQDQGHUH

EHGUDJHQVWRUWKRHODQJGXXUWKHWYRRUGDWHURSGHUHNHQLQJ

VWDDW"

$DQJH]LHQHUJHHQUHJHOPDWLJHEHWDOLQJHQZRUGHQJHGDDQ307 LV

GHEHWDOLQJVPRGXV(LQGRI%HJLQQLHWYDQEHODQJ

Toetsen: Display: Beschrijving:

0,00

:LVWDOOHUHJLVWHUV

1 1,00

6WHOW3<5JHOLMNDDQ

DDQJH]LHQGHUHQWHMDDUOLMNV

ZRUGWVDPHQJHVWHOG

–2.000,00

6ODDWKHWEHGUDJRSYDQKHW

HHUVWHGHSRVLWR

3.000,00

6ODDWKHWEHGUDJRSGDWXZLOW

ELMHHQVSDUHQ

7,20

6ODDWGHMDDUOLMNVHUHQWHYRHW

RS

5,83

%HUHNHQWKHWDDQWDOMDUHQGDW

QRGLJLVRPRSWH

NRPHQ

10B.book Page 61 Wednesday, June 28, 2000 3:31 PM

62 5: “Time Value of Money”-berekeningen

$DQJH]LHQGHEHUHNHQGHZDDUGHYDQ1WXVVHQHQOLJW]LMQHU

WHQPLQVWH]HVMDUHQMDDUOLMNVHDFFXPXODWLHQRGLJRPRSWHQPLQVWHWH

NRPHQ%HUHNHQKHWZHUNHOLMNHVDOGRQD]HVMDDU

Voorbeeld: Een persoonlijke pensioenrekening. 8KHEWRSDSULO

HHQSHUVRRQOLMNHSHQVLRHQUHNHQLQJJHRSHQGHQGDDURS

JHVWRUW(UZRUGWDIJHKRXGHQYDQXZORRQHQXZRUGWWZHHPDDO

SHUPDDQGXLWEHWDDOG2SGHUHNHQLQJZRUGWMDDUOLMNVUHQWHEHWDDOG

GLHSHUKDOYHPDDQGZRUGWJHDFFXPXOHHUG+RHYHHO]DOHURSDSULO

RSGHUHNHQLQJVWDDQ"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

6,00

6WHOW RSMDDULQ

3.035,28

%HUHNHQWKHWEHGUDJ

GDWXQDMDDUNXQW

RSQHPHQ

10B.book Page 62 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 63

Voorbeeld: Een annuïteitenrekening. 1DHHQVXFFHVYROOH

]DNHQFDUULqUHEHVOXLWXWHJDDQUHQWHQLHUHQ8KHEWJHVSDDUG

ZDDURYHUXHHQJHPLGGHOGHMDDUOLMNVHUHQWHYDQNULMJWGLHPDDQGHOLMNV

ZRUGWVDPHQJHVWHOG+RHJURRWLVKHWEHGUDJGDWXDDQKHWHLQGYDQ

LHGHUHPDDQGNXQWRSQHPHQDOVXZLOWGDWXZVSDDUUHNHQLQJXJHGXUHQGH

GHYROJHQGHMDDURQGHUVWHXQW"

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHLQGLFDWRUQLHW]LHW

Toetsen: Display: Beschrijving:

24,00

6WHOWKHWDDQWDOSHULRGHVSHU

MDDULQ

–2.000,00

6ODDWGHHHUVWHVWRUWLQJRS

–80,00

6ODDWGHUHJHOPDWLJH

KDOIPDDQGHOLMNVHVWRUWLQJHQ

RS

6,30

6ODDWGHUHQWHYRHWRS

360,00

6ODDWKHWDDQWDOVWRUWLQJHQRS

52.975,60

%HUHNHQWKHWWHJRHG

10B.book Page 63 Wednesday, June 28, 2000 3:31 PM

64 5: “Time Value of Money”-berekeningen

Leaseberekeningen

(HQOHDVHLVHHQOHQLQJYDQZDDUGHYROOHJRHGHUHQ]RDOVYDVWJRHGDXWR·V

RIJHUHHGVFKDSJHGXUHQGHHHQEHSDDOGHWLMGWHJHQUHJHOPDWLJH

EHWDOLQJHQ6RPPLJHOHDVHFRQWUDFWHQZRUGHQXLWJHVFKUHYHQDOV

NRRSDNWHVPHWHHQRSWLHRPDDQKHWHLQGHYDQGHOHDVHSHULRGHWHNRSHQ

VRPVYRRUDPSHU'HYDVWJHVWHOGHWRHNRPVWLJHZDDUGH)9 YDQ

GHJRHGHUHQDDQKHWHLQGYDQHHQOHDVHZRUGWVRPVGH´UHVLGXZDDUGHµRI

´XLWNRRSZDDUGHµJHQRHPG

$OOHYLMI790WRHSDVVLQJVWRHWVHQNXQQHQELMOHDVHEHUHNHQLQJHQJHEUXLNW

ZRUGHQ(U]LMQWZHHDOJHPHHQYRRUNRPHQGHOHDVHEHUHNHQLQJHQ

+HWEHUHNHQHQYDQGHOHDVHEHWDOLQJRPHHQEHSDDOGHRSEUHQJVWWH

YHUNULMJHQ

+HWEHUHNHQHQYDQGHKXLGLJHZDDUGHJHNDSLWDOLVHHUGHZDDUGHYDQ

HHQOHDVH

'HHHUVWHEHWDOLQJYRRUHHQOHDVHJHEHXUWJHZRRQOLMNDDQKHWEHJLQYDQGH

HHUVWHSHULRGH'DDURPZRUGWHUELMGHPHHVWHOHDVHEHUHNHQLQJHQLQGH

%HJLQPRGXVJHZHUNW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ

JHQSHUMDDULQ

–400.000,00

6ODDWXZDSSHOWMHYRRU

GHGRUVWDOVHHQXLW

JDDQGHGHSRVLWRRS

7,00

6ODDWGHMDDUOLMNVHUHQW

HYRHWRSGLHXGHQNWWH

NULMJHQ

600,00

6ODDWKHWDDQWDO

RSQDPHVRS

0,00

6ODDWKHWWHJRHGQD

MDDURS

2.392,80

%HUHNHQWKHWEHGUDJ

GDWXDDQKHWEHJLQYDQ

LHGHUHPDDQGNXQW

RSQHPHQ

10B.book Page 64 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 65

Voorbeeld: Het berekenen van een leasebetaling. (HQNODQWZLO

YRRUHHQDXWRHHQOHDVHRYHUHHQNRPVWYDQRYHUGULHMDDUDIVOXLWHQ

'HRYHUHHQNRPVWRPYDWHHQRSWLHRPGHDXWRDDQKHWHLQGYDQGH

OHDVHSHULRGHWHNRSHQWHJHQ'HHHUVWHPDDQGHOLMNVHEHWDOLQJLV

EHWDDOEDDURSGHGDJGDWGHNODQWLQJHEUXLNQHHPW$OVXHHQMDDUOLMNVH

RSEUHQJVWYDQPDDQGHOLMNVVDPHQJHVWHOGZLOWKHEEHQZDW]LMQGDQ

GHEHWDOLQJHQ"%HUHNHQGHEHWDOLQJYDQXLWXZVWDQGSXQWDOVGHDOHU

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHLQGLFDWRUQLHW]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ

JHQSHUMDDULQ

10,00

6ODDWGHJHZHQVWHMDDU

OLMNVHRSEUHQJVWRS

–13.500,00

6ODDWGHOHDVHSULMVRS

7.500,00

6ODDWGHUHVLGXZDDUGH

XLWNRRSZDDUGHRS

36,00

6ODDWGHGXXUYDQGH

OHDVHLQPDDQGHQRS

253,99

%HUHNHQWGHPDDQ

GHOLMNVHEHWDOLQJHQ

10B.book Page 65 Wednesday, June 28, 2000 3:31 PM

66 5: “Time Value of Money”-berekeningen

8]LHWGDW]HOIVDOVGHNODQWGHDXWRQLHWZHQVWWHNRSHQHUDDQKHWHLQG

YDQGHOHDVHHHQFDVKIORZELQQHQNRPWGLHJHOLMNLVDDQGHUHVLGXZDDUGH

YDQGHDXWR2IGHNODQWGHDXWRQXNRRSWRIGDWGHDXWRRSGHYULMH

PDUNWZRUGWYHUNRFKWGHOHDVHJHYHUYHUZDFKWHHQRSEUHQJVWYDQ

Voorbeeld: Lease met vooruitbetalingen. 8ZEHGULMI.ZLN7LPPHU

ZLOHHQYRUNKHIWUXFNOHDVHQYRRUGHRSVODJSODDWV'HOHDVHZRUGW

RSJHPDDNWYRRUHHQWHUPLMQYDQMDDUPHWPDDQGHOLMNVHEHWDOLQJHQYDQ

%HWDOLQJHQZRUGHQDDQKHWEHJLQYDQGHPDDQGEHWDDOEDDUJHVWHOG

HQGHHHUVWHHQODDWVWHEHWDOLQJPRHWHQELMKHWLQJDDQYDQGHOHDVH

YHUUHNHQGZRUGHQ8KHEWGHRSWLHRPDDQKHWHLQGYDQGHOHDVHSHULRGH

GHYRUNKHIWUXFNWHNRSHQWHJHQ

$OVGHMDDUOLMNVHUHQWHYRHWLVZDWLVGDQGHJHNDSLWDOLVHHUGHZDDUGH

YDQGHOHDVH"

'H]HEHUHNHQLQJZRUGWLQYLHUVWDSSHQRSJHORVW

 %HUHNHQGHKXLGLJHZDDUGHYDQGHPDDQGHOLMNVHDIEHWDOLQJHQ

ï² 

 7HOGDDUELMGHZDDUGHYDQGHH[WUDYRRUXLWEHWDOLQJRS

 %HUHNHQGHKXLGLJHZDDUGHYDQGHNRRSRSWLH

 7HOGHZDDUGHQXLWSXQWHQELMHONDDURS

10B.book Page 66 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 67

Punt 1%HUHNHQGHKXLGLJHZDDUGHYDQGHPDDQGHOLMNVHDIEHWDOLQJHQ

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHLQGLFDWRUQLHW]LHW

Punt 2. 7HOGHH[WUDYRRUXLWEHWDOLQJELM39RS6ODKHWUHVXOWDDWRS

Punt 3. %HUHNHQGHKXLGLJHZDDUGHYDQGHNRRSRSWLH

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ

JHQSHUMDDULQ

47,00

6ODDWKHWDDQWDO

EHWDOLQJHQRS

–2.400,00

6ODDWGHPDDQGHOLMNVH

EHWDOLQJRS

0,00

6ODDW)9YRRUSXQW

RS

9,00

6ODDWGHUHQWHYRHWRS

95.477,55

%HUHNHQWGHKXLGLJH

ZDDUGHYDQGH

PDDQGHOLMNVHEHWDOLQ

JHQ

97.877,55

7HOWGHH[WUDYRRUXLWEH

WDOLQJRS

97.877,55

6ODDWKHWUHVXOWDDWLQ

KHW0UHJLVWHURS

48,00

6ODDWGHPDDQGRS

ZDQQHHUGHNRRSRSWLH

ZRUGWXLWJHYRHUG

0,00

6ODDWHHQEHWDOLQJYDQ

QXORSYRRUGLWSXQW

YDQGHRSORVVLQJ

–15.000,00

6ODDWGHZDDUGHRSGLH

YHUGLVFRQWHHUGPRHW

ZRUGHQ

10.479,21

%HUHNHQWGHKXLGLJH

ZDDUGHYDQGHODDWVWH

FDVKIORZ

10B.book Page 67 Wednesday, June 28, 2000 3:31 PM

68 5: “Time Value of Money”-berekeningen

Punt 4. 7HOGHUHVXOWDWHQYDQSXQWHQELMHONDDURS

Amortisatie

$PRUWLVDWLHLVKHWYHUGHOHQYDQKHWEHGUDJYDQHHQ

EHWDOLQJLQHHQJHGHHOWHGDWEHWUHNNLQJKHHIWRSGHUHQWH

HQHHQJHGHHOWHGDWEHWUHNNLQJKHHIWRSGHKRRIGVRP

%HWDOLQJHQDDQKHWEHJLQYDQGHOHQLQJEHVWDDQXLWHHQ

JURWHUGHHODDQUHQWHHQXLWHHQNOHLQHUGHHODDQGH

KRRIGVRPGDQEHWDOLQJHQDDQKHWHLQGYDQHHQOHQLQJ

Toetsen: Display: Beschrijving:

108.356,77

%HUHNHQWGHKXLGLJH

JHNDSLWDOLVHHUGH

ZDDUGHYDQGHOHDVH

$IURQGLQJVYHUVFKLOOHQ

ZRUGHQRSSDJLQD 

YHUNODDUG

10B.book Page 68 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 69

0HWGH WRHWVYDQGH+3%,,NXQWXKHWYROJHQGHEHUHNHQHQ

+HWEHGUDJGDWLQHHQUHHNVEHWDOLQJHQEHWUHNNLQJKHHIWRSGHUHQWH

+HWEHGUDJGDWLQHHQUHHNVEHWDOLQJHQEHWUHNNLQJKHHIWRSGH

KRRIGVRP

+HWVDOGRYDQGHOHQLQJQDHHQEHSDDOGDDQWDOEHWDOLQJHQ

'H

IXQFWLHJDDWHUYDQXLWGDWX]RMXLVWHHQEHWDOLQJKHEWEHUHNHQG

RIGDWXGHEHWUHIIHQGHDPRUWLVDWLHZDDUGHQLQ,<539)9307HQ3

<5KHEWRSJHVODJHQ

'HJHWDOOHQGLHYRRUGHUHQWHGHKRRIGVRPHQKHWVDOGRZRUGHQJHWRRQG

]LMQDIJHURQGQDDUGHKXLGLJHLQVWHOOLQJYDQGHGLVSOD\

Het amortiseren. 8DPRUWLVHHUWHHQHQNHOYRXGLJHEHWDOLQJGRRUKHW

QXPPHUYDQGHEHWUHIIHQGHSHULRGHLQWHYXOOHQHQRS

WHGUXNNHQ

'H+3%,,WRRQWGHLQGLFDWRU

PERJHYROJGGRRUGHHHUVWHHQODDWVWH

EHWDOLQJHQGLH]XOOHQZRUGHQJHDPRUWLVHHUG

'UXNRS

RPGHUHQWHINTWHWRQHQ'UXNQRJPDDOVRS RPGH

KRRIGVRP

PRINWHWRQHQHQQDQRJPDDOVWHGUXNNHQ]LHWXKHWVDOGR



BAL'RRUWHONHQVRS WHGUXNNHQNXQWXGH]HOIGHZDDUGHQRSQLHXZ

EHNLMNHQ

8DPRUWLVHHUWHHQUHHNVEHWDOLQJHQGRRUKHWHHUVWHSHULRGHQXPPHU

ODDWVWH

SHULRGHQXPPHULQWHYRHUHQHQYHUYROJHQVRS

WHGUXNNHQ'H+3

%,,WRRQWGHLQGLFDWRU

PERJHYROJGGRRUGHHHUVWHHQODDWVWH

EHWDOLQJHQGLH]XOOHQZRUGHQJHDPRUWLVHHUG'UXNYHUYROJHQVWHONHQVRS

RPUHQWHKRRIGVRPHQVDOGRWHEHNLMNHQ

'UXNQRJPDDOVRS

RPQDDUGHYROJHQGHJURHSSHULRGHVWHJDDQ

'RRUGH]HDXWRPDWLVFKHYHUKRJLQJKRHIWXQLHWVLQWHWRHWVHQYRRUGH

QLHXZHEHJLQHQHLQGSHULRGH

$OVXWLMGHQVKHWDPRUWLVHUHQRSVODDWRSYUDDJWRIHQLJHDQGHUHEHZHUNLQJ

XLWYRHUWNULMJWXGRRURS

WHGUXNNHQUHQWHKRRIGVRPHQVDOGRQLHW

PHHUWH]LHQ$OVXGHDPRUWLVDWLHZHHUZLOWXLWYRHUHQPHWGH]HOIGH

SHULRGHVGUXNWXRS



-DDUOLMNVHQRPLQDOHUHQWHYRHW

%HJLQVDOGR

(LQGVDOGR

%HWDOLQJVEHGUDJDIJHURQGRSKHWGLVSOD\IRUPDDW

$DQWDOEHWDOLQJHQSHUMDDU

10B.book Page 69 Wednesday, June 28, 2000 3:31 PM

70 5: “Time Value of Money”-berekeningen

Voorbeeld: Een reeks betalingen amortiseren. %HUHNHQGHHHUVWH

WZHHMDDUYDQKHWMDDUOLMNVHDPRUWLVDWLHVFKHPDYRRUHHQK\SRWKHHNYDQ

RYHUHHQSHULRGHYDQMDDUWHJHQHHQMDDUOLMNVHUHQWHYRHWYDQ

PHWPDDQGHOLMNVHEHWDOLQJHQ

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

$OVXDOZHHWKRHJURRWGHEHWDOLQJRSGHK\SRWKHHNLVNXQWXGLW

LQYRHUHQHQRSVODDQ]RDOVXGHDQGHUHYLHUZDDUGHQRSVODDW$PRUWLVHHU

QXKHWHHUVWHMDDU

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ

JHQSHUMDDULQ

360,00

6ODDWKHWDDQWDOEHWDOLQ

JHQRS

7,75

6ODDWGHUHQWHSHUMDDU

RS

180.000,00

6ODDWGHKXLGLJHZDDUGH

RS

0,00

6ODDWGHWRHNRPVWLJH

ZDDUGHRS

–1.289,54

%HUHNHQWGHPDDQ

GHOLMNVHEHWDOLQJ

12_

9RHUWGHEHJLQHQ

HLQGSHULRGHVLQ

1– 12

7RRQWGH3(5LQGLFD

WRUHQUHHNV

–1.579,82

7RRQWGH35,1LQGLFD

WRUHQGHKRRIGVRPGLH

LQKHWHHUVWHMDDULV

EHWDDOG

–13.894,66

7RRQWGH,17LQGLFD

WRUHQGHUHQWHGLHLQ

KHWHHUVWHMDDULV

EHWDDOG

178.420,18

7RRQWGH%$/LQGLFD

WRUHQKHWVDOGRYDQGH

OHQLQJQDppQMDDU

10B.book Page 70 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 71

+HWEHGUDJGDWDDQUHQWHHQKRRIGVRPLVEHWDDOG 

LVJHOLMNDDQPDDQGHOLMNVHEHWDOLQJHQï 

+HWRSHQVWDDQGHVDOGRLVJHOLMNDDQGHEHJLQK\SRWKHHNPLQ

KHWEHGUDJGDWYRRUGHKRRIGVRPLVEHWDDOG² 



$PRUWLVHHUKHWWZHHGHMDDU

+HWEHGUDJGDWDDQUHQWHHQKRRIGVRPLVEHWDDOG 

LVJHOLMNDDQPDDQGHOLMNVHEHWDOLQJHQï 

+HWRSHQVWDDQGHVDOGRLVJHOLMNDDQGHEHJLQK\SRWKHHNPLQ

KHWEHGUDJGDWYRRUGHKRRIGVRPLVEHWDDOG²²

 (UZRUGWLQKHWWZHHGHMDDUPHHUDDQGH

KRRIGVRPEHWDDOGGDQLQKHWHHUVWHMDDU'HYROJHQGHMDUHQZRUGHQRS

GH]HOIGHZLM]HEHUHNHQG

13– 24

7RRQW3(5HQGHYRO

JHQGHUHHNVSHULRGHV

–1.706,69

7RRQW35,1HQGH

KRRIGVRPGLHLQKHW

WZHHGHMDDULVEHWDDOG

–13.767,79

7RRQW,17HQGHUHQWH

GLHLQKHWWZHHGHMDDULV

EHWDDOG

176.713,49

7RRQW%$/HQKHW

VDOGRYDQGHOHQLQJQD

EHWDOLQJHQ

10B.book Page 71 Wednesday, June 28, 2000 3:31 PM

72 5: “Time Value of Money”-berekeningen

Voorbeeld: Een enkelvoudige betaling amortiseren. $PRUWLVHHU

GH

 HQ EHWDOLQJYDQHHQYLMIMDDUGXUHQGH

DXWROHDVH+HWEHGUDJYDQGHOHDVHLVHQGHUHQWHYRHWLV

%HWDOLQJHQJHEHXUHQPDDQGHOLMNVHQHULVJHHQXLWVWHOYDQ

GHHHUVWHEHWDOLQJ

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHLQGLFDWRUQLHW]LHW

$PRUWLVHHUGH

 HQ EHWDOLQJHQ

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

60,00

6ODDWKHWDDQWDOEHWDOLQJHQRS

11,50

6ODDWGHUHQWHSHUMDDURS

14.250,00

6ODDWGHKXLGLJHZDDUGHRS

0,00

6ODDWGHWRHNRPVWLJHZDDUGH

RS

–310,42

%HUHNHQWGHPDDQGHOLMNVH

EHWDOLQJ

1,00

9RHUWGHHHUVWHEHWDOLQJLQ

1– 1

7RRQW3(5HQGHJHDPRUWL

VHHUGHEHWDOLQJVSHULRGH

–310,42

7RRQW35,1HQGHHHUVWH

EHWDOLQJDDQGHKRRIGVRP

0,00

7RRQW,17HQGHUHQWH

13.939,58

7RRQW%$/HQKHWVDOGRYDQ

GHOHQLQJQDppQEHWDOLQJ

25,00

9RHUWGHWHDPRUWLVHUHQEHWDO

LQJLQ

25– 25

7RRQW3(5HQGHJHDPRUWL

VHHUGHEHWDOLQJVSHULRGH

–220,21

7RRQW35,1HQGHKRRIGVRP

GLHELMGH

EHWDOLQJLV

EHWDDOG

–90,21

7RRQW,17HQGHUHQWHGLH

RYHUGH

EHWDOLQJLV

EHWDDOG

10B.book Page 72 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 73

Rentevoetconversies

%LMGHFRQYHUVLHYDQGHUHQWHYRHWZRUGHQGULHWRHWVHQ

JHEUXLNW

 HQ 'H]HFRQYHUWHUHQ

QRPLQDOHUHQWHQDDUMDDUOLMNVHHIIHFWLHYHUHQWHHQWHUXJ

1RPLQDOHHQHIIHFWLHYHUHQWHZRUGHQRSSDJLQD 

EHVFKUHYHQ

$OVXZHHWKRHKRRJHHQMDDUOLMNVHQRPLQDOHUHQWHLVHQX

GHGDDUPHHRYHUHHQNRPHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYRHWZLOW

EHUHNHQHQGRHWXKHWYROJHQGH

 9RHUGHQRPLQDOHUHQWHLQHQGUXNRS



 9RHUKHWDDQWDOSHULRGHVLQZDDURYHUVDPHQJHVWHOGPRHWZRUGHQHQ

GUXNRS



 %HUHNHQGHHIIHFWLHYHUHQWHYRHWGRRURS

WHGUXNNHQ

+HWEHUHNHQHQYDQHHQQRPLQDOHUHQWHGLHRYHUHHQNRPWPHWHHQEHNHQGH

HIIHFWLHYHUHQWH

 9RHUGHHIIHFWLHYHUHQWHLQHQGUXNRS



 9RHUKHWDDQWDOSHULRGHVLQZDDURYHUPRHWZRUGHQVDPHQJHVWHOGHQ

GUXNRS



 %HUHNHQGHQRPLQDOHUHQWHYRHWGRRURS

WHGUXNNHQ

9.193,28

7RRQW%$/HQKHWVDOGRYDQ

GHOHQLQJQDGH

EHWDOLQJ

54,00

9RHUWGHWHDPRUWLVHUHQEHWDO

LQJLQ

54– 54

7RRQW3(5HQGHJHDPRUWL

VHHUGHEHWDOLQJVSHULRGH

–290,37

7RRQW35,1HQGHKRRIGVRP

GLHELMGH

EHWDOLQJLV

EHWDDOG

–20,05

7RRQW,17HQGHUHQWHGLH

RYHUGH

EHWDOLQJLV

EHWDDOG

1.801,57

7RRQW%$/HQKHWVDOGRYDQ

GHOHQLQJQDGH

EHWDOLQJ

10B.book Page 73 Wednesday, June 28, 2000 3:31 PM

74 5: “Time Value of Money”-berekeningen

%LMGH790WRHSDVVLQJJHEUXLNHQ HQ KHW]HOIGHUHJLVWHU

5HQWHFRQYHUVLHVZRUGHQKRRIG]DNHOLMNELMWZHHVRRUWHQSUREOHPHQ

JHEUXLNW

9RRUKHWYHUJHOLMNHQYDQLQYHVWHULQJHQPHWYHUVFKLOOHQGHSHULRGHV

ZDDURYHUGHUHQWHZRUGWVDPHQJHVWHOG

9RRUKHWRSORVVHQYDQ790SUREOHPHQZDDUELMGHEHWDOLQJVSHULRGH

HQGHUHQWHSHULRGHYHUVFKLOOHQ

Investeringen met verschillende periodes van

samenstelling

Voorbeeld: Investeringen vergelijken. 8RYHUZHHJWHHQ

VSDDUUHNHQLQJWHRSHQHQHQXNXQWNLH]HQXLWGULHEDQNHQ:HONHEDQN

ELHGWGHEHVWHUHQWHYRRUZDDUGHQ"

Eerste bank

Tweede bank

(HUVWHEDQN MDDUOLMNVHUHQWHYRHWSHUNZDUWDDOVDPHQJHVW

HOG

7ZHHGHEDQN MDDUOLMNVHUHQWHYRHWPDDQGHOLMNVVDPHQJHVWHOG

'HUGHEDQN MDDUOLMNVHUHQWHYRHWNHHUSHUMDDU

VDPHQJHVWHOG

Toetsen: Display: Beschrijving:

6,70

6ODDWGHQRPLQDOHUHQWHRS

4,00

'HUHQWHZRUGWYLHUPDDOSHU

MDDUVDPHQJHVWHOG

6,87

%HUHNHQWGHMDDUOLMNVHHIIHF

WLHYHUHQWHYRHW

6,65

6ODDWGHQRPLQDOHUHQWHRS

12,00

6ODDWGHPDDQGHOLMNVHSHULRGHV

RSZDDULQZRUGWVDPHQJHVWHOG

6,86

%HUHNHQWGHMDDUOLMNVHHIIHFWLHYH

UHQWHYRHW

10B.book Page 74 Wednesday, June 28, 2000 3:31 PM

5: “Time Value of Money”-berekeningen 75

Derde bank

+HWDDQERGYDQGHHHUVWHEDQNLVLHWVEHWHURPGDWJURWHULVGDQ

HQ

Samenstellings- en betalingsperiodes verschillen

'H790WRHSDVVLQJJDDWHUYDQXLWGDWGH

VDPHQVWHOOLQJVSHULRGHVHQGHEHWDOLQJVSHULRGHVJHOLMN]LMQ

6RPPLJHOHQLQJVWHUPLMQHQHQGHSRVLWR·VHQRSQDPHVYDQ

VSDDUUHNHQLQJHQNRPHQQLHWXLWPHWGH

VDPHQVWHOOLQJVSHULRGHVYDQGHEDQN$OVGH

EHWDOLQJVSHULRGHYHUVFKLOWYDQGHVDPHQVWHOOLQJVSHULRGH

SDVWXGHUHQWHYRHWDDQ]RGDWGLHPHWGHEHWDOLQJVSHULRGH

RYHUHHQNRPWYRRUGDWXKHWSUREOHHPRSORVW

8JDDWDOVYROJWWHZHUNDOVXGHUHQWHYRHWZLOWDDQSDVVHQZDQQHHUGH

VDPHQVWHOOLQJVSHULRGHYHUVFKLOWYDQGHEHWDOLQJVSHULRGH

 9RHUGHQRPLQDOHUHQWHLQHQGUXNRS

9RHUKHWDDQWDO

SHULRGHVSHUMDDULQZDDULQZRUGWVDPHQJHVWHOGHQGUXNRS



%HUHNHQGHHIIHFWLHYHUHQWHYRHWGRRURS

WHGUXNNHQ

 9RHUKHWDDQWDOEHWDOLQJVSHULRGHVSHUMDDULQHQGUXNRS

%HUHNHQ

GHDDQJHSDVWHQRPLQDOHUHQWHGRRURS

WHGUXNNHQ

6,63

6ODDWGHQRPLQDOHUHQWHRS

360,00

6ODDWGHSHULRGHVRSZDDULQ

ZRUGWVDPHQJHVWHOG

6,85

%HUHNHQWGHMDDUOLMNVHHIIHFWLHYH

UHQWHYRHW

10B.book Page 75 Wednesday, June 28, 2000 3:31 PM

76 5: “Time Value of Money”-berekeningen

Voorbeeld: Maandelijkse betaling, dagelijks samenstellen. 9DQDI

YDQGDDJVWRUWXPDDQGHOLMNVRSHHQUHNHQLQJZDDURYHUUHQWH

ZRUGWEHWDDOGGLHGDJHOLMNVZRUGWVDPHQJHVWHOGGDJHQSHUMDDU:DW

LVKHWVDOGRQD]HYHQMDDU"

Punt 1. %HUHNHQGHRYHUHHQNRPVWLJHUHQWHELMPDDQGHOLMNVH

VDPHQVWHOOLQJ

$DQJH]LHQ120HQ,<5KHW]HOIGHUHJLVWHUJHEUXLNHQNXQWXGH]H

ZDDUGHGLUHFWLQGHUHVWYDQKHWYUDDJVWXNJHEUXLNHQ

Punt 2. 'HWRHNRPVWLJHZDDUGHEHUHNHQHQ

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHLQGLFDWRUQLHW]LHW

Toetsen: Display: Beschrijving:

5,00

6ODDWKHWSHUFHQWDJH

YDQGHQRPLQDOHUHQWH

RS

365,00

6ODDWKHWDDQWDO

SHULRGHVRSZDDULQGH

EDQNVDPHQVWHOW

5,13

%HUHNHQWGHMDDUOLMNVH

HIIHFWLHYHUHQWHYRHW

12,00

6ODDWGHPDDQGHOLMNVH

SHULRGHVRS

5,01

%HUHNHQWKHW

RYHUHHQNRPVWLJH

QRPLQDOHSHUFHQWDJH

ZDQQHHUPDDQGHOLMNV

ZRUGWVDPHQJHVWHOG

0,00

6ODDWGHKXLGLJHZDDUGH

RS

–25,00

6ODDWGHEHWDOLQJRS

84,00

6ODDWKHWDDQWDO

EHWDOLQJHQSHUMDDURS

2.519,61

%HUHNHQWKHWVDOGRQD

MDDU

10B.book Page 76 Wednesday, June 28, 2000 3:31 PM

6: Cashflowberekeningen 77

Cashflowberekeningen

Het gebruiken van de cashflowfunctie

'HFDVKIORZIXQFWLHZRUGWJHEUXLNWELMKHWRSORVVHQYDQ

YUDDJVWXNNHQZDDUELMFDVKIORZVPHWUHJ HOPDWLJH

WXVVHQSR]HQYRRUNRPHQPDDUYHUVFKLOOHQGYDQJU RRWWH

]LMQ8NXQWRRNFDVKIORZE HUHNHQLQJHQ XLWYRHUHQRP

YUDDJVWXNNHQPHWUHJHOPDWLJHHYHQJ URWHSHULRGLHNH

FDVKIORZVRSWHORVVHQ PDDUGH]HVLWXDWLHVNXQQ HQ

HIILFLsQWHUZRUGHQRSJ HORVWPHW790

,QKHWDOJHPHHQZRUGHQGHYROJHQ GHSXQWHQXLWJHYRHUGELM

FDVKIORZEHUHNHQLQJHQRSGH+3%,,

 % HNLMNXZFDVKI ORZVRSSDS LHU(HQFDVKIORZGLDJUDPNDQKH HO

KDQGLJ]LMQ

 :LVGHUHJLVWHUV

 9RHUKHWDDQWDOSHULRGHVSH UMDDULQ

 9RHUGHLQLWLsOHLQYHVWHULQJHQLQ 

 9RHUKHWEHGUDJYDQGHYROJHQGHFDVKI ORZLQ

 $OVKHWEHGUDJGDWXLQSXQWKHEWLQJHYRHUGPHHUGDQHH QVQD

HONDDUYRRUNRPWYRHUGDQKHWDDQWDONHUHQLQGDWGLWEHGUDJ

YRRUNRPW

 +HUKDDOSXQWHQYRRULHGHUHFDVKI ORZHQJURHS

 8EHUHNHQWGHQHWWRKXLGLJHZDDUGHGRRUGHMDDUOLMNVHUHQ WHYRHWRS

WHYRHUHQHQRS

WHGUXNNHQYHUYROJHQVGUXNWXRS $OVX

KHWMDDUOLMNVHLQWHUQHUHQGHPHQWZLOWEHUHNHQHQGUXNWXRS



10B.book Page 77 Wednesday, June 28, 2000 3:31 PM

78 6: Cashflowberekeningen

Voorbeeld: Een investering op korte termijn. ,QKHWYROJHQGH

FDVKIORZGLDJUDP]LHWXHHQLQYHVWHULQJLQDDQGHOHQRYHUGULHPDDQGHQ

DIJHEHHOG$DQKHWEHJLQYDQLHGHUHPDDQGZHUGHQDDQNRSHQJHGDDQHQ

GHDDQGHOHQZHUGHQDDQKHWHLQGYDQGHPDDQGYHUNRFKW%HUHNHQKHW

MDDUOLMNVHLQWHUQHUHQGHPHQWHQKHWPDDQGHOLMNVHUHQGHPHQW

XXX

Toetsen: Display: Beschrijving:

0,00

:LVWDOOHUHJLVWHUV

12,00

6ODDWSHULRGHVSHUMDDURS

–5.000.00

9RHUWGHHHUVWHFDVKIORZLQ

7RRQWKHWQXPPHUYDQGH

FDVKIORZJURHSWHUZLMOX



LQJHGUXNWKRXGW

–2.000.00

9RHUWGHYROJHQGHFDVKIORZLQ

–4.000,00

9RHUWGHYROJHQGHFDVKIORZLQ

11.765,29

9RHUWGHODDWVWHFDVKIORZLQ

38,98

%HUHNHQWGHMDDUOLMNVHQRPLQDOH

RSEUHQJVW

3,25

0DDQGHOLMNVHRSEUHQJVW

10B.book Page 78 Wednesday, June 28, 2000 3:31 PM

6: Cashflowberekeningen 79

NPV en IRR/YR: Het verdisconteren van

cashflows

,QKRRIGVWXNVWDDWDDQJHJHYHQKRHFDVKIORZGLDJUDPPHQJHEUXLNW

NXQQHQZRUGHQRPILQDQFLsOHYUDDJVWXNNHQWHYHUKHOGHUHQ,QGH]H

SDUDJUDDIZRUGHQYHUGLVFRQWHHUGHFDVKIORZVEHVSURNHQ'H139HQ

,55<5IXQFWLHVZ RUGHQRRNYDDNYHUGLVFRQWHHUGHFDVKIORZIXQFWLHVJHQRHPG

'RRUHHQFDVKIORZWHYHUGLVFRQWHUHQEHUHNHQWXGHKXLGLJHZDDUGHYDQ

GHFDVKIORZ:DQQHHU PHHUFDVKIORZVZRUGHQYHUGLVFRQWHHUGEHUHNHQWX

GHKXLGLJHZDDUGHQGDDUYDQHQWHOWXGLHELMHONDDURS

'HQHWWRKXLGLJHZDDUGHIXQFWLH139EHUHNHQWGHKXLGLJHZ DDUGHYDQ

HHQDDQWDOFDVKIORZV'HMDDUOLMNVHQRPLQDOHUHQWHYRHWPRHWEHNHQG]LMQ

RP139WHNXQQHQEHUHNHQHQ

'HLQWHUQHUHQGHPHQWIXQFWLH,55<5EHUHNHQWGHMDDUOLMNVHQRPLQDOH

UHQWHYRHWZDDUPHHHHQQHWWRKXLGLJHZDDUGHYDQQXOYHUNUHJHQZ RUGW

+HWQXWYDQGH]HWZHHILQDQFLsOHEHJULSSHQZRUGWGXLGHOLMNQDKHW

XLWZHUNHQYDQHHQSDDUY RRUEHHOGHQ,QGHYROJHQGHWZHHSDUDJUDIHQ

NRPWKHWJURHSHUHQHQLQYRHUHQYDQFDVKIORZVDDQGHRUGH'DDUQD

YROJHQHQNHOHYRRUEHHOGHQYDQ139HQ,55<5EHUHNHQLQJHQ

Cashflows groeperen

(HQUHHNVYDQFDVKIORZVZRUGWJHJURHSHHUGLQHHQHHUVWH FDVKIORZ&)HQ

GDDURSYROJHQGHFDVKIORZJURHSHQPD[LPDDOFDVKIORZV&)NRPWDDQ

KHWEHJLQYDQGHHHUVWHSHULRGH(HQFDVKIORZJURHSEHVWDDWXLWKHWEHGUDJ

ZDDUXLWGHFDVKIORZEHVWDDWHQKHWDDQWDOKHUKDOLQJHQ

,QKHWYROJHQGHFDVKIORZGLDJUDPLVGHHHUVWHFDVKIORZELMYRRUEHHOG

²'HYROJHQGHJURHSFDVKIORZVEHVWDDWXLW]HVFDVKIORZVYDQHON

QXOJHYROJGGRRUHHQJURHS YDQGULHFDVKIORZVYDQHON'HODDWVWH

JURHSEHVWDDWXLWppQFDVKIORZYDQ

10B.book Page 79 Wednesday, June 28, 2000 3:31 PM

80 6: Cashflowberekeningen

:DQQHHUXHHQV HULHFDVKIORZVLQYRHU WLVKHWYDQEHODQ JGDWLHGHUH

FDVKIORZLQKHWFDVKIORZGLDJU DPZRUGWYDVWJHOHJG]HOIVELMSHULRGHVPHW

HHQFDVKIORZYDQ QXO

Cashflows invoeren

,QGH+3%,,NXQWXHHQHHUVWHFDVKIORZRSVODDQHQGDDUQDQRJ

H[WUDFDVKIORZJURHSHQ(ONHFDVKIORZJURHSNDQWRWFDVKIORZV

EHYDWWHQ8YRHUWFDVKIORZVDOVYROJWLQ

 'UXNRS

RPGHUHJLVWHUVWHZLVVHQ

 9RHUKHWDDQWDOSHULR GHVSHUMDDULQHQGUXNRS



 9RHUKHWEHGUDJYDQGHHHUVWHLQYHVWHULQJLQHQGUXNYHUYROJHQVRS

'H´MµJHHIWKHWQXPPHUYDQGHFDVKIORZDDQWRWHQPHW

 9RHUKHWEHGUDJYDQGHYROJHQGHFDVKIORZLQHQGUXNRS



 $OVKHWEHGUDJGDWLQSXQWZHUGLQJHYRHUGPHHUGDQHHQVQDHONDDU

YRRUNRPWYRHUWXLQKRHYDDNGLWJHEHXUWHQGUXNWXRS



 +HUKDDOSXQWHQYRRULHGHUH

HQ WRWGDWDOOHFDVKIORZV

]LMQLQJHYRHUG

10B.book Page 80 Wednesday, June 28, 2000 3:31 PM

6: Cashflowberekeningen 81

Voorbeeld. 9RHUGHFDV KI ORZVYDQKHWYRRUJDDQGHGLDJU DPLQ HQ

EHUHNHQGH,5 5<5%HUHNHQYHU YROJHQVGHHII HFWLHYHUHQWH1HHPDDQ

GDWHUSHULRGHVSHUMDDU]LMQ 

Cashflows bekijken en vervangen

8NXQWHHQOLMVWPHWFDVKIORZVEHNLMNHQGRRURSGHYROJHQGHWRHWVHQWH

GUXNNHQ

WRW RPFDVKIORZVWRWWHEHNLMNHQRI

WRW RPFDVKIORZVWRWZHHUWHJHYHQ

RPGHYROJHQGHFDVKIORZWH]LHQ

RPGHYRULJHFDVKIORZWH]LHQRI

RPGHKXLGLJHFDVKIORZWH]LHQ

Toetsen: Display: Beschrijving:

0,00

:LVWDOOHUHJLVWHUV

12,00

6WHOW RSLQ

–11.000,00

9RHUWGHHHUVWHFDVKIORZLQ

7RRQWKHWQXPPHUYDQGH

FDVKIORZJURHSWHUZLMOX



LQJHGUXNWKRXGW

0,00

9RHUWKHWEHGUDJYDQGHHHUVWH

FDVKIORZJURHSLQ

6,00

9RHUWKHWDDQWDONHUHQLQGDWGLW

ZRUGWKHUKDDOG

1.000,00

9RHUWKHWEHGUDJYDQGHWZHHGH

FDVKIORZJURHSLQ

3,00

9RHUWKHWDDQWDONHUHQLQGDWGLW

ZRUGWKHUKDDOG

10.000,00

9RHUWGHODDWVWHFDVKIORZLQ

21,22

%HUHNHQWGHMDDUOLMNVHQRPLQDOH

RSEUHQJVW

10B.book Page 81 Wednesday, June 28, 2000 3:31 PM

82 6: Cashflowberekeningen

2PKHWEHGUDJYDQHHQFDVKIORZWHYHUYDQJHQGUXNWXRS

WRW RPKHWQLHXZHEHGUDJRSWHVODDQLQFDVKIORZV

WRWRI

WRW RPKHWQLHXZHEHGUDJRSWHVODDQLQFDVKIORZV

WRW

RPKHWEHGUDJRSWHVODDQLQGHYROJHQGHFDVKIORZ

RPKHWEHGUDJRSWHVODDQLQGHYRULJHFDVKIORZ

RPKHWEHGUDJRSWHVODDQLQGHKXLGLJHFDVKIORZ

$OVXKHWDDQWDONHUHQGDWHHQFDVKIORZYRRUNRPWZLOWDDQSDVVHQ

GH

FDVKIORZZDDUYRRUXGLWZLOWGRHQ9RHUYHUYROJHQVKHWDDQWDONHUHQLQ

GDWGH]HPRHWYRRUNRPHQHQGUXNRS



$DQJH]LHQFDVKIORZVQLHWYHUZLMGHUGRIWXVVHQJHYRHJGNXQQHQZRUGHQ

JHEUXLNWX

RPRSQLHXZWHEHJLQQHQ

De netto huidige waarde berekenen

'HQHWWRKXLGLJHZDDUGHIXQFWLH1 39ZRUGWJHEUXLNWRPDOOH

FDVKIORZVWHYHUGLVFRQWHUHQGLHYRRUGHWLMGOLMQVWDDQPHWEHKXOSYDQHHQ

MDDUOLMNVHQRPLQDOHUHQWHYRHWGLHXLQYRHU W

+LHURQGHU]LHWXKRHX139EHUHNHQW

 'UXNRS

VODKHWDDQWDOSHULRGHVSHUMDDULQ3<5RS

 9RHUGHFDVKI ORZVLQPHW

HQ 

 6ODGHMDDUOLMNVHQRPLQDOHUHQWHYRHWLQ,<5RSHQGUXNRS



Voorbeeld: Een verdisconteerd contract, ongelijke cashflows. 8

NXQWHHQFRQWUDFWNRSHQPHWGHYROJHQGHFDVKIORZV

Eind van de maand Bedrag

 

 

 

 

 

10B.book Page 82 Wednesday, June 28, 2000 3:31 PM

6: Cashflowberekeningen 83

:DWPRHWXYRRUKHWFRQWUDFWE HWDOHQDOVXHHQMDDUOLMNVUHQGHPH QWYDQ

RSXZLQYHVWHULQJZLOWKDOHQ"

Toetsen: Display: Beschrijving:

0,00

:LVWGHUHJLVWHUV

12,00

6WHOWKHWDDQWDOEHWDOLQJHQS HU

MDDULQ

0,00

9RHUWGHHHUVWHFDVKIORZYDQ

QXOLQ8]LHWKHWQXPPHUYDQ

GHFDVKIORZWHUZLMOX



LQJHGUXNWKRXGW

0,00

9RHUWGHHHUVWHFDVKIORZLQ

3,00

9RHUWKHWDDQWDONHUHQLQGDW

GH]HYRRUNRPW

5.000,00

9RHUWGHWZHHGHFDVKIORZLQ

0,00

9RHUWGHGHUGHFDVKIORZLQ

4,00

9RHUWKHWDDQWDONHUHQLQGDW

GH]HYRRUNRPW

5.000,00

9RHUWGHYLHUGHFDVKIORZLQ

2,00

9RHUWKHWDDQWDONHUHQLQGDW

GH]HYRRUNRPW

0,00

9RHUWGHYLMIGHFDVKIORZLQ

4,00

9RHUWKHWDDQWDONHUHQLQGDW

GH]HYRRUNRPW

7.500,00

9RHUWGH]HVGHFDVKIORZLQ

0,00

9RHUWGH]HYHQGHFDVKIORZLQ

9,00

9RHUWKHWDDQWDONHUHQLQGDW

GH]HYRRUNRPW

10.000,00

9RHUWGHYROJH QGHFDVKIORZLQ

10B.book Page 83 Wednesday, June 28, 2000 3:31 PM

84 6: Cashflowberekeningen

'HFDVKIORZVGLHXZWRHNRP VWLJHLQYHVWHULQJEHVFKULMYHQVWDDQQXLQGH

FDOFXODWRU8NXQWRS

GU XNNHQHQGDDUQDRS HQELM

KHUKDOLQJRS

RPGHFDVKIORZVHQ KHWDDQWDONHUHQGDWGH]H

YRRUNRPHQWHEHNLMNHQ

1DGDWXGHFDVKIORZVKHEWLQJHYRHUGVODDWXGHU HQWHYRHWRSHQEHUHNHQW

XGHQHWWRKXLGLJHZDDUGH

8LWKHWUHVXOWDDWEOLMNWGDWDOVXHHQUHQGHPHQ WYDQSHUMDDUZLOW

KHEEHQXYRRUKHWFRQWU DFWPRHWEHWDOHQ8]LHWGDWGLWHHQ

SRVLWLHIEHGUDJLV'HQHWWRKXLGLJHZDDUGHEHVWDDWXLWGHELMHONDDU 

RSJHWHOGHZDDUGHQYDQ HHQVHULHYDQFDV KIORZVZDQQHHU]LMQDDUKHWEHJLQ

YDQGHWLMGOLMQZR UGHQYHUGLVFRQWHHUG

Toetsen: Display: Beschrijving:

15,00

6ODDWGHJHZHQVWH

MDDUOLMNVHUHQWHYRHWRS

27.199,92

%HUHNHQWGHQHWWR

KXLGLJHZDDUGHYDQ

LHGHUHFDVKIORZGLHLV

RSJHVODJHQ=LHKHW

YRRUEHHOGRYHU

DIURQGHQRS

SDJLQD 

10B.book Page 84 Wednesday, June 28, 2000 3:31 PM

6: Cashflowberekeningen 85

Het interne rendement berekenen

 'UXNRS VODKHWDDQWDOSHULRGHVSHUMDDULQ3<5RS

 9RHUGHFDVKIORZVLQPHW

HQ 

 'UXNRS



$OVX,55<5E HUHNHQWNULMJWXGHMDDUOLMNVHQRPLQDOHUHQWHGLHXHHQ

139 YDQQXOJHHIW

,QKHWYROJHQGHYRRUEHHOGZRUGHQGH]HOIGHFDVKIORZVJHEUXLNWDOV ELMKHW

YRULJHYRRUEHHOG

(ULVPHHUGDQppQ,55<5PRJHOLMN$OVXGHPHOGLQJ

no SoLution

NULMJWUDDGSOHHJGDQ$DQKDQJVHO%SDJLQD 

Voorbeeld. $OVGHYHUNRSHUYDQKHWFRQWUDFWXLWKHWYRU LJHYRRUEHHOG

YHUODQJWHQXDFFHSWHHUWGLHSULMVZDWLVGDQXZUHQGHPHQW"'LW

LVHHQ,55<5EHUHNHQLQJZDDUYRRUHHQNOHLQHYHUDQGHULQJDDQGHRSGLW

RJHQEOLNRSJHVODJHQFDVKIORZVQRGLJLV

8YLQGWQRJPHHUYRRUEHHOGHQZDDULQ139HQ,55<5YRRUNRPHQLQ

KRRIGVWXN´([WUDYRRUEHHOGHQµ

Toetsen: Display: Beschrijving:

–28.000,00

:LM]LJWGHHHUVWHFDVKIORZ

12,49

%HUHNHQWGHMDDUOLMNVHQRPLQDOH

RSEUHQJVW

10B.book Page 85 Wednesday, June 28, 2000 3:31 PM

86 6: Cashflowberekeningen

Automatische opslag van IRR/YR en NPV

$OVXGH139EHUHNHQWZRUGWKHWUHVXOWDDWLQ39RSJHVODJHQ$OVXGDW

UHVXOWDDWZLOWRSYUDJHQGUXNWXRS

$OVXGH790ZDDUGHQXLW KHW

ODDWVWHYRRUEHHOGZDDULQPHW139ZHUGJHZHUNWSDJLQD QLHWKHEW

YHUDQGHUGLVKHWUHVXOWDDWDOVXRS

GUXNW

$OVX,55<5EHUHNHQWZRUGWKHWUHVXOWDDWRRNLQ,<5RSJHVODJHQ%LM

KHWYRULJHYRRUEHHOGGUXNWXRS

RPGHMDDUOLMNVHRSEUHQJVW

WHWRQHQ

10B.book Page 86 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 87

Statistische berekeningen

'HWRHWVHQ HQ ZRUGHQJHEUXLNWRPJHJHYHQV

YRRUVWDWLVWLHNHQPHWppQRIWZHHYDULDEHOHQLQWHYRHUHQRI

WHYHUZLMGHUHQ6RPPDWLHJHJHYHQVZRUGHQRSJHVODJHQLQ

KHWJHKHXJHQ'HODEHOVGLHERYHQGH

WRW WRHWVHQ

VWDDQJHYHQDDQZHONVWDWLVWLVFKJHJHYHQLQKHWEHWUHIIHQGH

UHJLVWHULVRSJHVODJHQ1DGDWXGHJHJHYHQVKHEWLQJHYRHUG

NXQWXGHVWDWLVWLVFKHIXQFWLHVJHEUXLNHQRPKHWYROJHQGH

WHEHUHNHQHQ

*HPLGGHOGHHQVWDQGDDUGGHYLDWLH

/LQHDLUHUHJUHVVLH

/LQHDLUHEHQDGHULQJHQYHUZDFKWLQJHQ

*HZRJHQJHPLGGHOGH

6RPPDWLHVWDWLVWLHNHQQ

[

[ 

\

\ HQ

[\

Statistische gegevens wissen

:LVGHVWDWLVWLVFKHUHJLVWHUVYRRUGDWXQLHXZHJHJHYHQV

LQYRHUW$OVXGHUHJLVWHUVQLHWZLVWZRUGHQGHJHJHYHQV

GLHRSGLWRJHQEOLN]LMQRSJHVODJHQDXWRPDWLVFK

RSJHQRPHQLQGHVRPPDWLHEHUHNHQLQJHQ8ZLVWGH

VWDWLVWLVFKHUHJLVWHUVGRRURS

WHGUXNNHQ'HGLVSOD\

ZRUGWGDQHYHQHHQVJHZLVW

10B.book Page 87 Wednesday, June 28, 2000 3:31 PM

88 7: Statistische berekeningen

Statistische gegevens invoeren

8NXQWHHQRQEHJUHQVGDDQWDOZDDUGHQLQGHVWDWLVWLVFKHUHJLVWHUV

YHU]DPHOHQ



Statistieken met één variabele

8JDDWDOVYROJWWHZHUNELMKHWLQYRHUHQYDQGH[JHJHYHQVELMVWDWLVWLHNHQ

PHWppQYDULDEHOH

 :LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS

WHGUXNNHQ

 9RHUGHHHUVWHZDDUGHLQHQGUXNRS

'H+3%,,WRRQWQKHW

DDQWDOYHU]DPHOGHJHJHYHQV

 *DYHUGHUPHWKHWWRHYRHJHQYDQZDDUGHQGRRUGHJHWDOOHQLQWH

YRHUHQHQRS

WHGUXNNHQ'HQZDDUGHZRUGWELMLHGHUHLQYRHU

YHUKRRJG

Statistieken met twee variabelen en gewogen

gemiddelde

8YRHUWDOVYROJW[\SDUHQYDQVWDWLVWLVFKHJHJHYHQVLQ

 :LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS

WHGUXNNHQ

 9RHUGHHHUVWH[ZDDUGHLQHQGUXNRS

'H+3%,,JHHIWGH[

ZDDUGHZHHU

 9RHUGHRYHUHHQNRPVWLJH\ZDDUGHLQHQGUXNRS

'H+3%,,

JHHIWQKHWDDQWDOYHU]DPHOGHSDUHQZHHU

 *DYHUGHUPHWKHWLQYRHUHQYDQ[\SDUHQ'HQZDDUGHZRUGWELM

LHGHUHLQYRHUYHUKRRJG

8YRHUWJHJHYHQVYRRUKHWEHUHNHQHQYDQKHWJHZRJHQJHPLGGHOGHLQ

GRRULHGHUHZDDUGHDOV[LQWHYRHUHQHQGHRYHUHHQNRPVWLJH

ZHJLQJVFRsIILFLsQWDOV\

Als door de statistische gegevens de waarde in een register groter wordt dan

9,99999999999 × 10

499

toont de HP 10BII een tijdelijke overflow melding (OFLO).

10B.book Page 88 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 89

Statistische gegevens verbeteren

2QMXLVWLQJHYRHUGHJHJHYHQVNXQQHQYHUZLMGHUGZRUGHQPHW $OV

ppQYDQGHZDDUGHQYDQHHQ[\SDDURQMXLVWLVPRHWXEHLGHZDDUGHQ

YHUZLMGHUHQHQRSQLHXZLQYRHUHQ

Verbeteren van gegevens bestaande uit één variabele

+HWYHUZLMGHUHQHQRSQLHXZLQYRHUHQYDQVWDWLVWLVFKHJHJHYHQVJDDWDOV

YROJW

 7RHWVGH[ZDDUGHLQGLHYHUZLMGHUGPRHWZRUGHQ

 'UXNRS

RPGHZDDUGHWHYHUZLMGHUHQ'HQZDDUGHZRUGW

PHWppQYHUPLQGHUG

 9RHUGHMXLVWHZDDUGHLQPHW



Verbeteren van gegevens bestaande uit twee

variabelen

+HWYHUZLMGHUHQHQRSQLHXZLQYRHUHQYDQ[\SDUHQVWDWLVWLVFKHJHJHYHQV

JDDWDOVYROJW

 9RHUGH[ZDDUGHLQGUXNRS

HQYRHUYHUYROJHQVGH\ZDDUGHLQ

 'UXNRS

RPGHZDDUGHQWHYHUZLMGHUHQ'HQZDDUGHZRUGW

PHWppQYHUPLQGHUG

 9RHUKHWMXLVWH[\SDDULQPHW

HQ 

10B.book Page 89 Wednesday, June 28, 2000 3:31 PM

90 7: Statistische berekeningen

Samenvatting van statistische berekeningen

6RPPLJHIXQFWLHVOHYHUHQWZHHZDDUGHQRS'HSTATLQGLFDWRUJHHIWDDQ

GDWWZHHZDDUGHQ]LMQEHUHNHQG'UXNRS

RPGHYHUERUJHQ

ZDDUGHWH]LHQ

Toetsen Beschrijving naar display

5HNHQNXQGLJ

JHPLGGHOGHYDQGH[

ZDDUGHQ

*HPLGGHOGHYDQGH\

ZDDUGHQDOVX\ZDDUGHQ

KHEWLQJHYRHUG

*HPLGGHOGHYDQGH[

ZDDUGHQJHZRJHQ

YROJHQVGH\ZDDUGHQ

6WHHNSURHIVWDQGDDUGGHYL

DWLHYDQGH[ZDDUGHQ

6WHHNSURHIVWDQGDDUGGHYL

DWLHYDQGH\ZDDUGHQDOV

X\ZDDUGHQKHEW

LQJHYRHUG

3RSXODWLHVWDQGDDUGGHYLD

WLHYDQGH[ZDDUGHQ

3RSXODWLHVWDQGDDUGGHYLD

WLHYDQGH\ZDDUGHQDOV

X\ZDDUGHQKHEW

LQJHYRHUG

\ZDDUGH

%HQDGHULQJYDQ[ELMHHQ

JHJHYHQZDDUGHYDQ\

&RUUHODWLHFRsIILFLsQW

[ZDDUGH %HQDGHULQJYDQ\ELMHHQ

JHJHYHQZDDUGHYDQ[

5LFKWLQJVFRsIILFLsQWP

YDQGHEHUHNHQGHOLMQ



VQLMSXQWPHWGH\DVEYDQ

GHEHUHNHQGHOLMQ

5LFKWLQJVFRsIILFLsQWP

YDQGHEHUHNHQGHOLMQ

10B.book Page 90 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 91

Gemiddelde, standaarddeviatie en

sommatiestatistieken

8NXQWKHWJHPLGGHOGH GH

VWHHNSURHIVWDQGDDUGGHYLDWLH6

HQ

SRSXODWLHVWDQGDDUGGHYLDWLH

HQVRPPDWLHVWDWLVWLHNHQ

Q

[HQ

[

YDQ[JHJHYHQVEHUHNHQHQ9RRUGH[\

JHJHYHQVNXQWXRRNKHWJHPLGGHOGHGH

VWHHNSURHIVWDQGDDUGGHYLDWLHHQGH

SRSXODWLHVWDQGDDUGGHYLDWLHYDQ\JHJHYHQVHQGH

VRPPDWLHVWDWLVWLHNHQ

\

HQ

[\EHUHNHQHQ

Voorbeeld 1. 'HNDSLWHLQYDQHHQMDFKWZLOEHSDOHQKRHYHHOWLMGKHWNRVW

RPHHQ]HLOWHYHUZLVVHOHQ=LMNLHVWKLHUYRRU]HVZLOOHNHXULJHOHGHQYDQ

KDDUEHPDQQLQJREVHUYHHUWKHQELMKHWZLVVHOHQYDQKHW]HLOHQVFKULMIW

KHWEHQRGLJGHDDQWDOPLQXWHQRS%HUHNHQKHW

JHPLGGHOGHHQGHVWDQGDDUGGHYLDWLHYDQGHWLMGHQ%HUHNHQRRNGHZRUWHO

XLWKHWJHPLGGHOGHYDQGHNZDGUDWHQPHWGHIRUPXOH 

Toetsen Beschrijving

$DQWDOLQJHYRHUGHJHJHYHQVSXQWHQ

6RPYDQGH[ZDDUGHQ

6RPYDQGH\ZDDUGHQ

6RPYDQGHNZDGUDWHQYDQGH[ZDDUGHQ

6RPYDQGHNZDGUDWHQYDQGH\ZDDUGHQ

6RPYDQGHSURGXFWHQYDQGH[DQG\

ZDDUGHQ

Toetsen: Display: Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV

1,00

9RHUWGHHHUVWHWLMGLQ

2,00

9RHUWGHWZHHGHWLMGLQ

3,00

9RHUWGHGHUGHWLMGLQ

4,00

9RHUWGHYLHUGHWLMGLQ

5,00

9RHUWGHYLMIGHWLMGLQ

[

n⁄

∑

10B.book Page 91 Wednesday, June 28, 2000 3:31 PM

92 7: Statistische berekeningen

'HVWDQGDDUGGHYLDWLHVGLH]LMQEHUHNHQGPHW HQ

 ]LMQGHVWHHNSURHIVWDQGDDUGGHYLDWLHV+LHUELM

ZRUGWDDQJHQRPHQGDWKHWRPHHQJURWHUHYROOHGLJH

YHU]DPHOLQJYDQJHJHYHQVJDDW

$OVGHJHJHYHQVGHJHKHOHSRSXODWLHYHUWHJHQZRRUGLJHQ

NDQGHZHUNHOLMNHSRSXODWLHVWDQGDDUGGHYLDWLHZRUGHQ

EHUHNHQGGRRURS

HQ WHGUXNNHQ

Voorbeeld 2. 'HFRDFKKHHIWYLHUQLHXZHVSHOHUVLQKHWWHDPGLH

HQFPODQJ]LMQHQHQNJZHJHQ%HUHNHQKHW

JHPLGGHOGHHQGHSRSXODWLHVWDQGDDUGGHYLDWLHYDQKXQOHQJWHHQJHZLFKW

HQVRPPHHUYHUYROJHQVGH\ZDDUGHQ

6,00

9RHUWGH]HVGHWLMGLQ

3,50

%HUHNHQWKHWJHPLGGHOGH

0,85

%HUHNHQWGHVWHHNSURHI

VWDQGDDUGGHYLDWLH

77,13

*HHIW

[ ZHHU

6,00

*HHIWQZHHU

3,59

%HUHNHQWKHWNZDGUDWLVFK

JHPLGGHOGH

Toetsen: Display: Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV

1,00

9RHUWGHOHQJWHHQKHW

JHZLFKWYDQVSHOHULQ

2,00

9RHUWGHOHQJWHHQKHW

JHZLFKWYDQVSHOHULQ

3,00

9RHUWGHOHQJWHHQKHW

JHZLFKWYDQVSHOHULQ

4,00

9RHUWGHOHQJWHHQKHW

JHZLFKWYDQVSHOHULQ

184,25

%HUHNHQWKHWJHPLGGHOGH

YDQGHOHQJWHV[

82,75

*HHIWKHWJHPLGGHOGH

YDQGHJHZLFKWHQZHHU

\

10B.book Page 92 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 93

Lineaire regressie en benadering

/LQHDLUHUHJUHVVLHLVHHQVWDWLVWLVFKHPHWKRGHYRRUKHW

PDNHQYDQEHQDGHULQJHQHQYHUZDFKWLQJHQ'HPHWKRGH

ZRUGWJHEUXLNWRPHHQUHFKWHOLMQWHYLQGHQGLH]RJRHG

PRJHOLMNGRRUHHQYHU]DPHOLQJ[\JHJHYHQVJHWURNNHQ

NDQZRUGHQ(UPRHWHQWHQPLQVWHWZHHYHUVFKLOOHQGH[\

SDUHQ]LMQ'HUHFKWHOLMQJHHIWGHUHODWLHWXVVHQGH[HQ\

YDULDEHOHQZHHU\ P[EZDDUELMPGH

ULFKWLQJVFRsIILFLsQWLVHQEKHWVQLMSXQWPHWGH\DV

Lineaire regressie. %HUHNHQPEHQUGHFRUUHODWLHFRsIILFLsQWDOVYROJW

 :LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS

WHGUXNNHQ

 9RHUGHHHUVWH[ZDDUGHLQHQGUXNRS

'H+3%,,JHHIWGH[

ZDDUGHZHHU

 9RHUGHRYHUHHQNRPVWLJH\ZDDUGHLQHQGUXNRS

'H+3%,,

JHHIWQKHWDDQWDOYHU]DPHOGHSDUHQZHHU

 *DYHUGHUPHWKHWLQYRHUHQYDQ[\SDUHQ'HQZDDUGHZRUGWELM

LHGHUHLQYRHUYHUKRRJG

 8YLQGWEKHWVQLMSXQWPHWGH\DVGRRURS

WHGUXNNHQ

9HUYROJHQVGUXNWXRS

RPPGHULFKWLQJVFRsIILFLsQWYDQGH

OLMQWHNULMJHQ

 8YLQGWUGHFRUUHODWLHFRsIILFLsQWGRRURS

WHGUXNNHQ

5,80

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OHQJWHV[

4,71

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HYDQGHJHZLFKWHQZHHU

\

331,00

*HHIWKHWWRWDDOYDQ\

ZHHU

10B.book Page 93 Wednesday, June 28, 2000 3:31 PM

94 7: Statistische berekeningen

Lineaire benadering. 'HUHFKWHOLMQGLHGRRUOLQHDLUHUHJUHVVLHLV

EHUHNHQGNDQZRUGHQJHEUXLNWRPHHQEHQDGHULQJYDQHHQ\ZDDUGHWH

YLQGHQELMHHQJHJHYHQ[ZDDUGHHQRPJHNHHUG

 9RHUGH[\JHJHYHQVLQYROJHQVGHLQVWUXFWLHVRSSDJLQD 

 9RHUGHEHNHQGH[ZDDUGHRI\ZDDUGHLQ

$OVXHHQEHQDGHULQJYDQ[ZLOWKHEEHQYRRUGHJHJHYHQ\YRHUW

XGH\ZDDUGHLQHQGUXNWXYHUYROJHQVRS



$OVX\ZLOWEHQDGHUHQYRRUHHQJHJHYHQ[YRHUWXGH[ZDDUGH

LQHQGUXNWXYHUYROJHQVRS



Voorbeeld: verwachtingen $OL·V$]DOHDVPDDNWUHFODPHRSHHQ

SODDWVHOLMNUDGLRVWDWLRQ*HGXUHQGHGHDIJHORSHQ]HVZHNHQKHHIWGHEDDV

ELMJHKRXGHQKRHYHHOPLQXWHQUHFODPHHUJHNRFKWZHUGHQHQKRHYHHO

D]DOHD·VHUGLHZHHN]LMQYHUNRFKW

%HUHNHQKHWVQLMSXQWPHWGH\DVGHULFKWLQJVFRsIILFLsQWHQGH

FRUUHODWLHFRsIILFLsQW

Week

Minuten reclame

(

-waarden)

Verkoop

(

-waarden)

  

  

  

  

  

  

10B.book Page 94 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 95

Toetsen: Display: Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV

1,00

9RHUWPLQXWHQHQYHUNRRS

LQYRRUGHDFKWHUHHQYRO

JHQGHZHNHQ

2,00

3,00

4,00

5,00

6,00

376,25

%HUHNHQWKHWVQLMSXQWPHW

GH\DVE

425,88

*HHIWGHULFKWLQJVFRsI

ILFLsQWZHHU

0,90

%HUHNHQWGHFRUUH

ODWLHFRsIILFLsQW

10B.book Page 95 Wednesday, June 28, 2000 3:31 PM

96 7: Statistische berekeningen

0DDNWHHQVFKDWWLQJYDQKHWYHUNRRSFLMIHUDOVKHWEHGULMIRIPLQXWHQ

UHFODPHNRRSW

+RHYHHOPLQXWHQUHFODPHPRHW$OL·VNRSHQRPHHQYHUNRRSFLMIHUYDQ

WHEHKDOHQ"

Gewogen gemiddelde

2SGHYROJHQGHPDQLHUZRUGWKHWJHZRJHQJHPLGGHOGHYDQ

JHJHYHQVSXQWHQEHUHNHQG[

[ «[ PHWELMEHKRUHQGH

ZHJLQJVFRsIILFLsQWHQ\

\ «\ 

 *HEUXLN

HQ RP[\SDUHQLQWHYRHUHQ'H\ZDDUGHQ]LMQGH

JHZLFKWHQYDQGH[ZDDUGHQ

 'UXNRS



Voorbeeld. %LMHHQRQGHU]RHNQDDUGHKXXUSULMVYDQHHQNDPHUIODWV

EOLMNWGDWIODWVYHUKXXUGZRUGHQYRRUKXXUSHUPDDQGYRRU

YRRUHQYRRU:DWLVGHJHPLGGHOGHKXXUSULMVSHU

PDDQG"

3.357,38

0DDNWHHQVFKDWWLQJ

YDQKHWYHUNRRSFLMIHU

DOVPLQXWHQUHFODPH

ZRUGHQJHNRFKW

3.783,25

0DDNWHHQVFKDWWLQJ

YDQKHWYHUNRRSFLMIHU

DOVPLQXWHQUHFODPH

ZRUGHQJHNRFKW

6,16

0DDNWHHQVFKDWWLQJ

YDQKHWDDQWDOPLQXWHQ

UHFODPHQRGLJYRRUHHQ

YHUNRRSFLMIHUYDQ



10B.book Page 96 Wednesday, June 28, 2000 3:31 PM

7: Statistische berekeningen 97

Toetsen: Display: Beschrijving:

0,00

:LVWKHWVWDWLVWLVFKH

JHKHXJHQ

1,00

9RHUWGHHHUVWHKXXUHQ

KHWGDDUELMEHKRUHQGH

JHZLFKWLQ

2,00

9RHUWGHWZHHGHKXXU

HQKHWGDDUELM

EHKRUHQGHJHZLFKWLQ

3,00

9RHUWGHGHUGHKXXUHQ

KHWGDDUELMEHKRUHQGH

JHZLFKWLQ

4,00

9RHUWGHYLHUGHKXXU

HQKHWGDDUELM

EHKRUHQGHJHZLFKWLQ

509,44

%HUHNHQWKHWJHZRJHQ

JHPLGGHOGH

10B.book Page 97 Wednesday, June 28, 2000 3:31 PM

10B.book Page 98 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 99

Extra voorbeelden

Economische toepassingen

Het vaststellen van een verkoopprijs

(HQPHWKRGHYRRUKHWYDVWVWHOOHQYDQGHYHUNRRSSULMVSHUHHQKHLGLVKHW

EHSDOHQYDQGHSURGXFWLHNRVWHQSHUHHQKHLGHQGH]HWHYHUPHQLJYXOGLJHQ

PHWKHWJHZHQVWHUHQGHPHQW2PWRWHHQQDXZNHXULJUHVXOWDDWWHNRPHQ

PRHWXDOOHNRVWHQGLHDDQKHWSURGXFW]LMQYHUERQGHQYDVWVWHOOHQ

0HWGHYROJHQGHIRUPXOHZRUGWGHSULMVSHUHHQKHLGEHUHNHQGRSEDVLV

YDQGHWRWDOHNRVWHQHQKHWUHQGHPHQW

35,-6 727$/(.267

$$17$/((1+('(1ï571





Voorbeeld. +HWNRVWRPHHQKHGHQWHSURGXFHUHQ8ZLOW

UHQGHPHQW:HONHSULMVPRHWXSHUHHQKHLGYUDJHQ"

Toetsen: Display: Beschrijving:

40,000.00

9RHUWGHNRVWHQLQ

20,00

%HUHNHQWGHNRVWHQSHU

HHQKHLG

24,00

%HUHNHQWGH

YHUNRRSSULMVSHU

HHQKHLG

10B.book Page 99 Wednesday, June 28, 2000 3:31 PM

100 8: Extra voorbeelden

Verwachtingen gebaseerd op historische gegevens

(HQPHWKRGHYRRUKHWEHSDOHQYDQYHUNRRSYHUZDFKWLQJHQ

SURGXFWLHNRVWHQRIXLWJDYHQLVKHWEHNLMNHQYDQKLVWRULVFKHWHQGHQVHQ

$OVXKLVWRULVFKHJHJHYHQVKHEWNDQKLHUGRRUHHQNURPPHJHWURNNHQ

ZRUGHQZDDUELMGHWLMGODQJVGH[DVORRSWHQGHKRHYHHOKHLGODQJVGH\

DV

Voorbeeld. :DWLVKHWYHUZDFKWHYHUNRRSFLMIHULQMDDU]HVHQ]HYHQ

JHJHYHQGHYROJHQGHYHUNRRSLQIRUPDWLH"

Jaar Verkoop $

1 10.000

211.210

3 13.060

4 16.075

5 20.590

Toetsen: Display: Beschrijving:

0,00

:LVWGHVWDWLVWLVFKH

UHJLVWHUV

1,00

9RHUWKHWHHUVWHMDDULQ

HQKHWYHUNRRSFLMIHU

2,00

9RHUWGHJHJHYHQVYDQ

KHWWZHHGHMDDULQ

3,00

*DDWYHUGHUPHWKHW

LQYRHUHQYDQJHJHYHQV

4,00

5,00

22.000,50

9HUZDFKWH

YHUNRRSFLMIHUYRRUMDDU

]HV

24.605,00

9HUZDFKWH

YHUNRRSFLMIHUYRRUMDDU

]HYHQ

10B.book Page 100 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 101

Kosten indien niet contant wordt betaald

(HQNRSHUNULMJWNRUWLQJELMFRQWDQWHEHWDOLQJDOVGHEHWDOLQJELQQHQHHQ

EHSDDOGHSHULRGHSODDWVYLQGW%LMYRRUEHHOGGHYHUPHOGLQJ´

1(7µRSGHIDFWXXUEHWHNHQWGDWGHNRSHUSURFHQWNDQDIWUHNNHQ

DOVGHEHWDOLQJELQQHQGDJHQSODDWVYLQGW$OVGHEHWDOLQJQLHWELQQHQ

GDJHQSODDWVYLQGWPRHWKHWJHKHOHEHGUDJYRRUGH

GDJEHWDDOG

]LMQ

0HWGHIRUPXOHKLHURQGHUNXQWXEHUHNHQHQZDWKHWXNRVWDOVXJHHQ

JHEUXLNPDDNWYDQNRUWLQJELMFRQWDQWHEHWDOLQJ'HNRVWHQZRUGHQ

EHUHNHQGDOVHHQMDDUOLMNVHUHQWHGLHYRRUKHWXLWVWHOOHQYDQGHEHWDOLQJLQ

UHNHQLQJZRUGWJHEUDFKW

.257LVKHWNRUWLQJVSHUFHQWDJHDOVGHEHWDOLQJYURHJZRUGWJHGDDQ

727'*1LVWKHWRWDOQXPEHURIGD\VXQWLOWKHELOOPXVWEHSDLG.257

'*1LVKHWDDQWDOGDJHQGDWGHNRUWLQJEHVFKLNEDDULV

Voorbeeld. 8RQWYDQJWHHQUHNHQLQJPHWGHYRRUZDDUGHQ

1(7:DWNRVWKHWXDOVXJHHQJHEUXLNPDDNWYDQGH

NRUWLQJVPRJHOLMNKHLG"

Toetsen: Display: Beschrijving:

72.000,00

%HUHNHQWGHWHOOHUYDQ

GHIRUPXOH

98,00

+DDNMHVEHSDOHQGH

YROJRUGHYDQ

EHUHNHQLQJ

36,73

%HUHNHQWGHNRVWHQYDQ

KHWQLHWJHEUXLNPDNHQ

YDQGHNRUWLQJDOVHHQ

MDDUOLMNVSHUFHQWDJH

.267

.257 



 .257

–()(

727'*1

.257'*1

)–()

--------------------------------------------------------------------------------------------------------------------------

10B.book Page 101 Wednesday, June 28, 2000 3:31 PM

102 8: Extra voorbeelden

Leningen en hypotheken

Enkelvoudige jaarlijkse rente

Voorbeeld. (HQJRHGHYULHQGKHHIWHHQOHQLQJQRGLJRPHHQ

RQGHUQHPLQJWHEHJLQQHQHQKHHIWXRPHHQOHQLQJYDQYRRU

GDJHQJHYUDDJG8OHHQWKHPKHWJHZHQVWHEHGUDJWHJHQ

HQNHOYRXGLJHMDDUOLMNVHUHQWHWHEHUHNHQRSEDVLVYDQGDJHQ+RHYHHO

UHQWHLVKLMXQDGDJHQVFKXOGLJHQZDWLVKLMXLQWRWDDOVFKXOGLJ"

'H]HIRUPXOHZRUGWJHEUXLNWYRRUKHWEHUHNHQHQYDQHHQHQNHOYRXGLJH

MDDUOLMNVHUHQWHRSEDVLVYDQGDJHQLQHHQMDDU

5(17(

Continue samenstelling van rente

'HIRUPXOHYRRUKHWEHUHNHQHQYDQGHHIIHFWLHYHUHQWHYRHWELMFRQWLQXH

VDPHQVWHOOLQJLV

8JDDWDOVYROJWWHZHUNDOVXHHQYUDDJVWXNPHWYRRUWGXUHQGH

VDPHQVWHOOLQJZLOWRSORVVHQ

 %HUHNHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYRHWPHWERYHQVWDDQGHIRUPXOH

 8JHEUXLNWyIGH]HHIIHFWLHYHUHQWHYRHWYRRUEHUHNHQLQJHQPHWHHQ

MDDUOLMNVHSHULRGH3<5 yIXFRQYHUWHHUWGH]HUHQWHYRHW]RGDW

GH]HLQXZEHWDOLQJVSHULRGHYDQWRHSDVVLQJLV,QKHWYROJHQGH

YRRUEHHOGLV3<5 ]RGDWXHHQQLHXZH120 PRHW

EHUHNHQHQPHWEHKXOSYDQGHUHQWHYRHWFRQYHUVLHWRHSDVVLQJZDDUELM

3<5JHOLMNLVDDQ

Toetsen: Display: Beschrijving:

0,10

6ODDWUHQWHRS

7,40

%HUHNHQWYHUVFKXOGLJGHUHQWH

457,40

%HUHNHQWWRWDDOYHUVFKXOGLJGH

EHGUDJ

%('5/(1,1* 5(17(

7(50/(1,1*,1'*1



-----------------------------------------------------------------------------------------------------------------------------------------------------

()) H

÷()



–()



×=

10B.book Page 102 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 103

Voorbeeld. 8KHEWRSKHWRJHQEOLNRSHHQUHNHQLQJVWDDQELM

'URRP,QYHVWHULQJHQZDDURSXMDDUOLMNVMDDUOLMNVFRQWLQX

JHFXPXOHHUGHUHQWHNULMJW$DQKHWHLQGYDQLHGHUHPDDQGVWRUWX

RSGHUHNHQLQJ:DWLVKHWVDOGRQDMDDU"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

0,18

'HHOWGHQRPLQDOH

UHQWHGRRU

1,20

9HUKHIWHWRWGHPDFKW



19,72

%HUHNHQWGHMDDUOLMNVH

HIIHFWLHYHUHQWHYRHW

19,72

6ODDWGHHIIHFWLHYH

UHQWHYRHWRS

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

18,14

%HUHNHQWGHMDDUOLMNVH

QRPLQDOHUHQWHYRRU

HHQPDDQGHOLMNVH

EHWDOLQJVSHULRGH

180,00

6ODDWKHWDDQWDO

PDDQGHQRS

–250,00

6ODDWGHUHJHOPDWLJH

EHWDOLQJRS

–4.572,80

6ODDWKHWKXLGLJHVDOGR

DOVHHQQHJDWLHYH

ZDDUGHRSDOVELMHHQ

LQLWLsOHLQYHVWHULQJ

297.640,27

%HUHNHQWKHWVDOGRYDQ

GHUHNHQLQJQD

EHWDOLQJHQJHGXUHQGH

MDDUPHWHHQUHQWH

YDQGLHFRQWLQX

JHFXPXOHHUGZRUGW

10B.book Page 103 Wednesday, June 28, 2000 3:31 PM

104 8: Extra voorbeelden

Opbrengst van een verdisconteerde (of premie-)

hypotheek

'HMDDUOLMNVHRSEUHQJVWYDQHHQYHUGLVFRQWHHUGHRISUHPLHK\SRWKHHNNDQ

ZRUGHQEHUHNHQGDOVGHYROJHQGHJHJHYHQVEHNHQG]LMQRRUVSURQNHOLMNH

K\SRWKHHNVRP39UHQWHYRHW,<5SHULRGLHNHEHWDOLQJ307

EDOORRQEHWDOLQJ)9HQKHWEHGUDJGDWYRRUGHK\SRWKHHNLVEHWDDOG

QLHXZH39

'HQNDDQGHDIVSUDDNRYHUKHWJHEUXLNYDQWHNHQVELMFDVKIORZVEHWDDOGH

EHGUDJHQ]LMQQHJDWLHIRQWYDQJHQEHGUDJHQ]LMQSRVLWLHI

Voorbeeld. (HQLQYHVWHHUGHUZLOHHQK\SRWKHHNRSQHPHQYDQ

WHJHQRYHUHHQSHULRGHYDQMDDU6LQGVGHK\SRWKHHNLVJHQRPHQ

]LMQHUPDDQGHOLMNVHDIEHWDOLQJHQJHGDDQ'HOHQLQJZRUGWDDQKHWHLQG

YDQKHWYLMIGHMDDUYROOHGLJEHWDDOGHHQEDOORQEHWDOLQJ:DWLVGH

RSEUHQJVWYRRUGHNRSHUDOVGHSULMVYDQGHK\SRWKHHNZDV"

Punt 1. %HUHNHQ307/HWHURSGDW)9 

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

9,00

6ODDWGHUHQWHYRHWRS

240,00

6ODDWKHWDDQWDO

PDDQGHQRS

–100.000,00

6ODDWKHW

RRUVSURQNHOLMNHEHGUDJ

YDQGHOHQLQJRS

0,00

9RHUWKHWEHGUDJLQGDW

QDMDDUEHWDDOGPRHW

ZRUGHQ

899,73

%HUHNHQWGH

UHJHOPDWLJHEHWDOLQJ

10B.book Page 104 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 105

Punt 2. 9RHUGHQLHXZHZDDUGHYDQ1LQZDDUPHHZRUGWDDQJHJHYHQ

ZDQQHHUGHEDOORQEHWDOLQJJHEHXUW%HUHNHQYHUYROJHQV)9KHWEHGUDJ

YDQGHEDOORQEHWDOLQJ

Punt 3. 9RHUGHQLHXZHZDDUGHQYDQ1HQ39LQEHUHNHQYHUYROJHQVGH

QLHXZH,<5YRRUGHYHUGLVFRQWHHUGHK\SRWKHHNPHWEDOORQEHWDOLQJ

Jaarlijks percentage voor een lening met kosten

+HWMDDUOLMNVSHUFHQWDJH$35QHHPWGHNRVWHQLQDDQPHUNLQJGLH

JHZRRQOLMNEHUHNHQGZRUGHQELMKHWDIVOXLWHQYDQHHQK\SRWKHHNHQ

ZDDUGRRUGHUHQWHYRHWLQZHUNHOLMNKHLGZRUGWYHUKRRRJG+HWZHUNHOLMNH

EHGUDJGDWGHK\SRWKHHNQHPHURQWYDQJW39ZRUGWHULPPHUVGRRU

YHUPLQGHUGWHUZLMOGHSHULRGLHNHEHWDOLQJHQJHOLMNEOLMYHQ'H$35NDQ

ZRUGHQEHUHNHQGDOVGHWHUPLMQYDQGHK\SRWKHHN1SHULRGHVGH

MDDUOLMNVHUHQWHYRHW,35GHK\SRWKHHNVRPQLHXZH39HQKHWEHGUDJ

YDQGHNRVWHQEHNHQG]LMQ

Toetsen: Display: Beschrijving:

899,73

5RQGWYRRUGH

QDXZNHXULJKHLGGH

EHWDOLQJRSWZHH

GHFLPDOHQDI

60,00

6ODDWKHWDDQWDO

EHWDOLQJHQWRWGH

EDOORQEHWDOLQJRS

88.706,74

%HUHNHQWGH

EDOORQEHWDOLQJZRUGW

ELMGHODDWVWHEHWDOLQJ

RSJHWHOG

Toetsen: Display: Beschrijving:

18,00

6ODDWKHWRYHUJHEOHYHQ

DDQWDOEHWDOLQJHQRS

–79.000,00

6ODDWGHSULMVYDQGH

K\SRWKHHNRS

20,72

%HUHNHQWGHRSEUHQJVW

YDQGH]H

YHUGLVFRQWHHUGH

K\SRWKHHN

10B.book Page 105 Wednesday, June 28, 2000 3:31 PM

106 8: Extra voorbeelden

'HQNDDQGHDIVSUDDNRYHUKHWJHEUXLNYDQWHNHQVELMFDVKIORZVEHWDDOGH

EHGUDJHQ]LMQQHJDWLHIRQWYDQJHQEHGUDJHQ]LMQSRVLWLHI

Voorbeeld: APR voor een lening waaraan kosten verbonden zijn.

9RRUHHQOHQLQJZRUGWNRVWHQLQUHNHQLQJJHEUDFKWELMKHWDIVOXLWHQ

YDQHHQK\SRWKHHN+RHKRRJLVGH$35DOVGHK\SRWKHHNVRP

LVHQHHQORRSWLMGKHHIWYDQMDDUPHWHHQMDDUOLMNVHUHQWHYRHWYDQ

JHEDVHHUGRSPDDQGHOLMNVHEHWDOLQJHQ"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

8,50

6ODDWGHUHQWHYRHWRS

360,00

6ODDWGHGXXUYDQGH

OHQLQJRS

160.000,00

6ODDWKHW

RRUVSURQNHOLMNHEHGUDJ

YDQGHOHQLQJRS

0,00

'HOHQLQJZRUGWLQ

MDDUYROOHGLJDIEHWDDOG

–1.230,26

%HUHNHQWGHEHWDOLQJ

160.000,00

9UDDJWKHWEHGUDJYDQ

GHOHQLQJRS

156.800

7UHNWKHW

NRVWHQSHUFHQWDJHDI

8,72

%HUHNHQW$35NRVWHQ

LQDDQPHUNLQJ

JHQRPHQ

10B.book Page 106 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 107

Voorbeeld: Lening zonder tussentijdse aflossing. 'H

DIVOXLWSURYLVLHYDQHHQMDULJHOHQLQJYDQPHWMDDUOLMNVH

UHQWH]RQGHUWXVVHQWLMGVHDIORVVLQJLV:DWEUHQJWGLWGHNUHGLHWJHYHURS"

1HHPDDQGDWPDDQGHOLMNVHEHWDOLQJHQRYHUGHUHQWHZRUGHQJHGDDQ

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

12,00

6ODDWGHUHQWHYRHWRS

120,00

6ODDWGHGXXUYDQGH

OHQLQJRS

1.000.000,00

6ODDWKHW

RRUVSURQNHOLMNHEHGUDJ

YDQGHOHQLQJRS

–1.000.000,00

9RHUWKHWEHGUDJLQGDW

DDQKHWHLQGHYDQGH

ORRSWLMGYHUVFKXOGLJG

LV%HWDOLQJHQEHVWDDQ

DOOHHQXLWUHQWHKHW

WRWDDOJHOHHQGHEHGUDJ

LVGXVYHUVFKXOGLJG

–10.000,00

%HUHNHQWGHEHWDOLQJHQ

GLHDOOHHQXLWUHQWH

EHVWDDQ

1.000.000,00

9UDDJWKHWEHGUDJYDQ

GHOHQLQJRS

970.000,00

7UHNWKHW

NRVWHQSHUFHQWDJHDI

12,53

%HUHNHQW$35

10B.book Page 107 Wednesday, June 28, 2000 3:31 PM

108 8: Extra voorbeelden

Lening met een afwijkende eerste periode

790EHUHNHQLQJHQJDDQRYHUILQDQFLsOHWUDQVDFWLHVZDDUELMLHGHUH

EHWDOLQJVSHULRGHHYHQODQJLV+HWNRPWHFKWHUYRRUGDWGHHHUVWHSHULRGH

QLHWHYHQODQJLVDOVGHUHVWHUHQGHSHULRGHV'HHHUVWHSHULRGHZRUGWVRPV

GHDIZLMNHQGHRIJHGHHOWHOLMNHHHUVWHSHULRGHJHQRHPG

$OVHURYHUGHHHUVWHDIZLMNHQGHSHULRGHUHQWHZRUGWEHUHNHQGZRUGW

GH]HJHZRRQOLMNDOVHQNHOYRXGLJHUHQWHEHUHNHQGGXVQLHWVDPHQJHVWHOG

+HWEHUHNHQHQYDQEHWDOLQJHQZDDUELMHHQDIZLMNHQGHHHUVWHSHULRGH

YRRUNRPWJDDWPHWGH+3%,,LQWZHHVWDSSHQ

 %HUHNHQKHWEHGUDJDDQHQNHOYRXGLJHUHQWHGDWLQGHHHUVWH

JHGHHOWHOLMNHSHULRGHYHUVFKXOGLJGLVHQWHOGLWELMKHWEHGUDJYDQGH

OHQLQJRS'LWLVGHQLHXZH398PRHWGHOHQJWHYDQGHHHUVWH

DIZLMNHQGHSHULRGHNXQQHQEHUHNHQHQDOVHHQGHHOYDQGHJHKHOH

SHULRGH%LMYRRUEHHOGHHQDIZLMNHQGHSHULRGHYDQGDJHQ]RXHHQ

SHULRGH]LMQDOVHUYDQZRUGWXLWJHJDDQGDWHHQKHOHSHULRGHHHQ

PDDQGYDQGDJHQLV

 %HUHNHQGHEHWDOLQJPHWEHKXOSYDQGHQLHXZH39ZDDUELM1JHOLMN

LVDDQKHWDDQWDOYROOHGLJHSHULRGHV*HEUXLNGH%HJLQPRGXVDOVKHW

DDQWDOGDJHQWRWGHHHUVWHEHWDOLQJNOHLQHULVGDQJHEUXLNDQGHUV

GH(LQGPRGXV

Voorbeeld. (HQOHQLQJYDQRYHUPDDQGHQKHHIWHHQMDDUOLMNVH

UHQWHYDQ$OVGHHHUVWHPDDQGHOLMNVHEHWDOLQJQDGDJHQZRUGW

JHGDDQZDWLVGDQGHPDDQGHOLMNVHEHWDOLQJXLWJDDQGHYDQPDDQGHQYDQ

GDJHQ"

,QGLWYRRUEHHOGLVGHDIZLMNHQGHHHUVWHSHULRGHGDJHQ

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

15,00

6ODDWGHUHQWHYRHWRS

1,25

%HUHNHQWGHSHULRGLHNH

UHQWHYRHW

0,67

9HUPHQLJYXOGLJWPHWHHQGHHO

YDQHHQSHULRGH

10B.book Page 108 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 109

Een autolening

Voorbeeld. 8NRRSWHHQQLHXZHDXWRYRRU8GRHWHHQ

DDQEHWDOLQJYDQHQGHUHVWHUHQGHJDDWXILQDQFLHUHQ'H

GHDOHUELHGWXWZHHPDQLHUHQZDDURSJHILQDQFLHUGNDQZRUGHQ

(HQMDULJHOHQLQJPHWHHQMDDUOLMNVHUHQWHYDQ

(HQMDULJHOHQLQJPHWHHQMDDUOLMNVHUHQWHYDQHQ

NRUWLQJ

,QZHONJHYDOEHWDDOWXPLQGHUYRRUGHDXWR"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

%HUHNHQGHHHUVWHRSWLH

30,00

%HUHNHQWKHWEHGUDJDDQ

HQNHOYRXGLJHUHQWHGDWYRRUGH

DIZLMNHQGHSHULRGH

YHUVFKXOGLJGLV

4.530,00

7HOWGH]HHQNHOYRXGLJHUHQWHELM

GHKXLGLJHZDDUGHRS

36,00

6ODDWGHWHUPLMQZDDURYHUGH

OHQLQJORRSWRS

0,00

9RHUWKHWEHGUDJLQGDWQD

EHWDOLQJHQQRJXLWVWDDW

–157,03

%HUHNHQWKHWEHGUDJYDQGH

EHWDOLQJ

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

36,00

6ODDWGHEHNHQGHZDDUGHQRS

12,500.00

0,00

3,50

6ODDWGHHHUVWHUHQWHRS

–366,28

%HUHNHQWGHEHWDOLQJ

–13.185,94

%HUHNHQWGHWRWDOHUHQWHHQ

KRRIGVRP

10B.book Page 109 Wednesday, June 28, 2000 3:31 PM

110 8: Extra voorbeelden

%HUHNHQGHWZHHGHRSWLH

'HHHUVWHRSWLHNRVWLHWVPLQGHU

“Canadese hypotheek”

%LM&DQDGHVHK\SRWKHNHQ]LMQGHEHWDOLQJVSHULRGHVHQGH

VDPHQVWHOOLQJVSHULRGHVQLHWJHOLMN'HUHQWHZRUGWKDOIMDDUOLMNV

VDPHQJHVWHOGWHUZLMOEHWDOLQJHQPDDQGHOLMNVJHEHXUHQ$OVXGH790

PRJHOLMNKHLGYDQGH+3%,,ZLOWJHEUXLNHQPRHWXHHQ&DQDGHVH

K\SRWKHHNIDFWRUEHUHNHQHQGLWLVHHQDDQJHSDVWHUHQWHYRHWHQGH]HLQ,<5

RSVODDQ

0HHULQIRUPDWLHRYHUUHQWHYRHWFRQYHUVLHVYLQGWXRS

´5HQWHYRHWFRQYHUVLHVµRSSDJLQD 

Voorbeeld. :HONHPDDQGHOLMNVHEHWDOLQJLVQRGLJRPHHQ&DQDGHVH

K\SRWKHHNYDQRYHUMDDUWHDPRUWLVHUHQDOVGHMDDUOLMNVH

UHQWHYRHWLV"

Toetsen: Display: Beschrijving:

11.500,00

6ODDWEHGUDJYDQOHQLQJ

PLQGHNRUWLQJRS

9,50

6ODDWGHWZHHGHUHQWH

RS

–368,38

%HUHNHQWGHEHWDOLQJ

–13.261,64

%HUHNHQWGHWRWDOH

UHQWHHQKRRIGVRP

Toetsen: Display: Beschrijving:

12,00

2,00

6ODDWKHWEHNHQGHQRPLQDOH

SHUFHQWDJHHQKHWDDQWDO

VDPHQVWHOOLQJVSHULRGHV

12,36

%HUHNHQWGHMDDUOLMNVHHIIHFWLHYH

UHQWHYRHW

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

11,71

%HUHNHQWGH&DQDGHVH

K\SRWKHHNIDFWRUDDQJHSDVWH

UHQWHYRHW

10B.book Page 110 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 111

TVM-berekeningen voor “wat als...”-scenario’s

(pQYDQGHPHHVWZDDUGHYROOHDVSHFWHQYDQGH790WRHSDVVLQJYDQGH

+3%,,LVKHWJHPDNZDDUPHHGH]HWRHSDVVLQJNDQZRUGHQJHEUXLNW

YRRUEHUHNLQJHQLQYHUEDQGPHW´ZDWDOVµVFHQDULR·VVLPXODWLHV(HQHUJ

FRXUDQWHVLPXODWLHLVGHYROJHQGH´:DWDOVGHUHQWHYRHWYHUDQGHUWLQ«"

2SZHONHPDQLHUEHwQYORHGWGDWPLMQEHWDOLQJ"µ1DGDWXHHQEHWDOLQJ

KHEWEHUHNHQGGLHRSHHQEHSDDOGHUHQWHYRHWLVJHEDVHHUGKRHIWXRP

RSGH]HYUDDJDQWZRRUGWHNULMJHQDOOHHQGHQLHXZHUHQWHYRHWLQWH

YXOOHQHQ307RSQLHXZWHEHUHNHQHQ

,QHHQSDDUYRRUEHHOGHQHHUGHULQGH]HKDQGOHLGLQJKDGGHQZHKHW

JHEUXLNWYRRUZDWDOVVFHQDULR·VDOHYHQDDQJHVWLSWPDDUKLHUYROJW

HHQPHHUXLWJHZHUNWYRRUEHHOG

Voorbeeld. 8VWDDWRSKHWSXQWRPYRRUGHDDQNRRSYDQHHQ

YDNDQWLHKXLVHHQK\SRWKHHNYDQRYHUMDDUWHRQGHUWHNHQHQ

'HMDDUOLMNVHQRPLQDOHUHQWHYRHWLV

Deel 1. +RHJURRW]LMQXZEHWDOLQJHQDDQKHWHLQGYDQGHPDDQG"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

130.000

360,00

6ODDWDQGHUHEHNHQGHZDDUGHQ

YDQGHK\SRWKHHNRS

–1.308,30

%HUHNHQWGHPDDQGHOLMNVH

EHWDOLQJYRRUGH&DQDGHVH

K\SRWKHHN

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

735.000,00

6ODDWGHEHNHQGH

ZDDUGHQRS

11,20

360,00

0,00

–7.110,88

%HUHNHQWGHEHWDOLQJ

10B.book Page 111 Wednesday, June 28, 2000 3:31 PM

112 8: Extra voorbeelden

Deel 2. 'HVDODULVVHQYDQXZEHGULMIZRUGHQJHZRRQOLMNHHQVLQGHWZHH

ZHNHQRSYULMGDJEHWDDOG'HEDQNJDDWHUPHHDNNRRUGYDQLHGHUH

VDODULVXLWNHULQJRSWHQHPHQRQJHYHHUGHKHOIWYDQHHQ

PDDQGHOLMNVHEHWDOLQJHQGHEHWDOLQJVSHULRGHGDDUELMDDQWHSDVVHQ

VDPHQVWHOOLQJVSHULRGHVSHUMDDU:DWLVGHQLHXZHORRSWLMGYDQGHOHQLQJ"

Deel 3. :DWJHEHXUWHUDOVXPDDQGHOLMNVHEHWDOLQJHQ]RXGRHQ]RDOVLQ

GHHOPDDU]RXRSWHUHQYRRUORRSWLMGYDQMDDU"+RHJURRW]RXLQGDW

JHYDOGHPDDQGVRP]LMQ":DW]RXHUWRWDDODDQUHQWHEHWDDOGZRUGHQELM

GLWFRQWUDFW"

–3.555,00

9RHUWGHQLHXZH

EHWDOLQJLQ

26,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

RSWZHHZHNHOLMNVH

EHWDOLQJHQ

514,82

%HUHNHQWKHWDDQWDO

WZHHZHNHOLMNVH

EHWDOLQJHQ

19,80

*HHIWKHWDDQWDOMDUHQ

ZHHUGDWQRGLJLVRP

GHOHQLQJDIWHORVVHQ

Toetsen: Display: Beschrijving:

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

180,00

6ODDWGHQLHXZH

ORRSWLMGRS

–8.446,53

%HUHNHQWGHEHWDOLQJELM

HHQNRUWHUHORRSWLMG

–1.520.374,70

%HUHNHQWGHWRWDOH

EHWDOLQJ

–785.374,70

*HHIWGHWRWDOHUHQWH

ZHHUGLHYRRUKHW

FRQWUDFWZRUGWEHWDDOG

10B.book Page 112 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 113

Sparen

Sparen voor hogere studies

6WHOGDWXQXYRRU]LHQLQJHQWUHIWRPLQGHWRHNRPVWHHQDDQWDOXLWJDYHQ

WHGRHQ(HQYRRUEHHOGKLHUYDQLVVSDUHQYRRUGHKRJHUHVWXGLHVYDQXZ

NLQGHUHQ2PWHNXQQHQEHSDOHQKRHYHHOXSHUSHULRGHPRHWVSDUHQ

PRHWXZHWHQZDQQHHUXKHWJHOGQRGLJKHEWKRHYHHOXQRGLJKHEWHQ

WHJHQZHONHUHQWHYRHWXXZVSDDUJHOGNXQWLQYHVWHUHQ

Voorbeeld. 8ZRXGVWHGRFKWHUJDDWRYHUMDDUQDDUGHXQLYHUVLWHLWHQX

EHJLQWQXWHVSDUHQRPKDDURSOHLGLQJWHEHWDOHQ=H]DOJHGXUHQGHYLHU

MDDUDDQKHWEHJLQYDQHONMDDUQRGLJKHEEHQ+HWIRQGVZRUGW

XLWJH]HWWHJHQSHUMDDUPDDQGHOLMNVVDPHQJHVWHOGHUHQWHHQXZLOW

PDDQGHOLMNVHEHWDOLQJHQGRHQWHEHJLQQHQDDQKHWHLQGYDQGHORSHQGH

PDDQG'HVWRUWLQJHQZRUGHQJHVWRSWDOV]LMKDDUVWXGLHVEHJLQW+RHYHHO

PRHWXSHUPDDQGVWRUWHQ"

'LWSUREOHHPZRUGWLQWZHHVWDSSHQRSJHORVW%HUHNHQHHUVWKHWEHGUDJ

GDWXQRGLJKHEWDOV]LMQDDUGHXQLYHUVLWHLWJDDW%HJLQPHWHHQ

UHQWHFRQYHUVLHGLWLVQRGLJRPGDWGHUHQWHPDDQGHOLMNVZRUGW

VDPHQJHVWHOG

Toetsen: Display: Beschrijving:

6WHOGH%HJLQPRGXVLQ'UXNRS DOVXGHBEGINLQGLFDWRUQLHW]LHW

9,00

6ODDWGHMDDUOLMNVHQRPLQDOH

UHQWHRS

12,00

6ODDWKHWDDQWDOSHULRGHVRS

ZDDULQPHWGH]HQRPLQDOHUHQWH

JHFXPXOHHUGZRUGW

9,38

%HUHNHQWGHMDDUOLMNVHHIIHFWLHYH

UHQWHYRHW

10B.book Page 113 Wednesday, June 28, 2000 3:31 PM

114 8: Extra voorbeelden

$OVGHUHQWHPDDUppQNHHUSHUMDDUZRUGWVDPHQJHVWHOG]LMQGHHIIHFWLHYH

UHQWHHQGHQRPLQDOHUHQWHJHOLMN

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRUQLHW

]LHW

*HEUXLNYHUYROJHQVGH]H39DOVGH)9YDQKHWYROJHQGH

FDVKIORZGLDJUDPHQEHUHNHQGH307

9,38

6ODDWGHHIIHFWLHYHUHQWH

DOVMDDUOLMNVHUHQWHRS

1,00

6WHOWppQEHWDOLQJSHU

MDDULQ

15.000,00

6ODDWGHMDDUOLMNVH

RSQDPHRS

4,00

6ODDWKHWDDQWDO

RSQDPHVRS

0,00

6ODDWKHWVDOGRQDYLHU

MDDURS

–52.713,28

6ODDWKHWEHGUDJRSGDW

QRGLJLVDOVXZGRFKWHU

DDQKDDURSOHLGLQJ

EHJLQW

10B.book Page 114 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 115

6WHOGH(LQGPRGXVLQ'UXNRS DOVXGHBEGINLQGLFDWRU]LHW

Kapitaaltoename die onbelast is todat deze wordt

opgenomen

0HWGH790WRHSDVVLQJNXQWXGHWRHNRPVWLJHZDDUGHYDQHHQ

EHODVWLQJYULMHRIXLWJHVWHOGHEHODVWLQJUHNHQLQJEHSDOHQ+HWKDQJWYDQGH

EHODVWLQJZHWHQXZLQNRPHQDIRI]RZHOGHUHQWHDOVGHKRRIGVRP

EHODVWLQJYULM]LMQ8NXQWEHLGHJHYDOOHQRSORVVHQ

'HNRRSNUDFKWYDQGLHWRHNRPVWLJHZDDUGHLVDIKDQNHOLMNYDQGHLQIODWLH

HQGHORRSWLMGYDQGHUHNHQLQJ

Voorbeeld. 8RYHUZHHJWHHQUHNHQLQJWHRSHQHQZDDUYDQGHEHODVWLQJ

ZRUGWXLWJHVWHOGPHWHHQGLYLGHQGYDQ$OVXJHGXUHQGHMDDU

DDQKHWEHJLQYDQLHGHUMDDULQYHVWHHUWKRHYHHOVWDDWHUGDQRSGH

UHNHQLQJELMSHQVLRQHULQJ"+RHYHHOKHEWXGDQLQWRWDDOJHVWRUW"+RHYHHO

UHQWHKHEWXJHNUHJHQ":DWLVGHZDDUGHYDQXZUHNHQLQJQDEHODVWLQJHQ

DOVXQDSHQVLRQHULQJEHODVWLQJEHWDDOW"*DHUYDQXLWGDWDOOHHQGH

UHQWHZRUGWEHODVWHQGDWGHKRRIGVRPYRRUKHWVWRUWHQLVEHODVW:DWLV

GHNRRSNUDFKWYDQGHUHNHQLQJXLWJHGUXNWLQGHKXLGLJHZDDUGHYDQGH

GROODUHQJHUHNHQGHPHWHHQLQIODWLHYDQ"

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRUQLHW

]LHW

52.713,28

6ODDWKHWEHGUDJRSGDW

XQRGLJKHEW

0,00

6ODDWKHWEHGUDJRS

ZDDUPHHXEHJLQW

12,00

6WHOWKHWDDQWDO

EHWDOLQJHQSHUMDDULQ

144,00

6ODDWKHWDDQWDO

VWRUWLQJHQRS

9,00

6ODDWGHUHQWHYRHWRS

–204,54

%HUHNHQWZDWHU

PDDQGHOLMNVJHVWRUW

PRHWZRUGHQ

10B.book Page 115 Wednesday, June 28, 2000 3:31 PM

116 8: Extra voorbeelden

Toetsen: Display: Beschrijving:

1,00

6WHOWppQEHWDOLQJSHU

MDDULQ

35,00

8,18

6ODDWKHWDDQWDO

SHULRGHVHQGH

UHQWHYRHWRS

0,00

6ODDWKHWEHGUDJRS

ZDDUPHHXEHJLQW

–2.000,00

6ODDWGHMDDUOLMNVH

EHWDOLQJRS

387.640,45

%HUHNHQWKHWEHGUDJ

GDWELMSHQVLRQHULQJRS

GHUHNHQLQJVWDDW

–70.000,00

%HUHNHQWKHWWRWDOH

EHGUDJGDWXRSKHW

PRPHQWYDQ

SHQVLRQHULQJJHVWRUW

KHEW

317.640,45

%HUHNHQWGHUHQWHGLH

GHUHNHQLQJKHHIW

RSJHEUDFKWELM

SHQVLRQHULQJ

47.646,07

%HUHNHQWEHODVWLQJ

RYHUGHUHQWH

339.994,39

%HUHNHQW)9QD

EHODVWLQJHQ

339.994,39

6ODDWWRHNRPVWLJH

ZDDUGHQDEHODVLQJHQ

LQ)9RS

–86.159,84

%HUHNHQW)9GH

KXLGLJHZDDUGHYDQGH

NRRSNUDFKWQD

EHODVWLQJHQXLWJDDQGH

YDQLQIODWLH

10B.book Page 116 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 117

Waarde van een belastbare pensioenrekening

%LMGLWSUREOHHPZRUGWGH790WRHSDVVLQJJHEUXLNWRPGHWRHNRPVWLJH

ZDDUGHYDQHHQEHODVWEDUHSHQVLRHQUHNHQLQJWHEHUHNHQHQZDDURSPHW

LQJDQJYDQYDQGDDJUHJHOPDWLJHMDDUOLMNVHEHWDOLQJHQZRUGHQJHGDDQ

%HJLQPRGXV+HWEHGUDJGDWMDDUOLMNVDDQEHODVWLQJZRUGWEHWDDOGZRUGW

XLWGHUHNHQLQJJHKDDOG*DHUYDQXLWGDWGHVWRUWLQJHQUHHGVEHODVW]LMQ

Voorbeeld. $OVXLHGHUMDDUJHGXUHQGHMDDULQYHVWHHUWHQ

GLYLGHQGNULMJWGDWDOVQRUPDDOLQNRPHQEHODVWZRUGWKRHYHHOVWDDWHUGDQ

RSGHUHNHQLQJELMSHQVLRQHULQJ"*DHUYDQXLWGDWHUGLYLGHQGSHU

MDDUZRUGWEHWDDOGKHWEHODVWLQJVSHUFHQWDJHLVHQGDWGHEHWDOLQJHQ

YDQGDDJEHJLQQHQ+RHJURRWLVGHNRRSNUDFKWYDQGDWEHGUDJLQ

KHGHQGDDJVHGROODUVXLWJDDQGHYDQHHQLQIODWLHYDQ"

6WHOGH%HJLQPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRUQLHW

]LHW

Toetsen: Display: Beschrijving:

1,00

6WHOWppQEHWDOLQJSHU

MDDULQ

35,00

6ODDWDDQWDO

EHWDOLQJVSHULRGHVRS

WRWDDQKHWSHQVLRHQ

5,89

%HUHNHQWGHUHQWHYRHW

YHUPLQGHUGPHWKHW

EHODVWLQJSHUFHQWDJH

5,89

6ODDWGHDDQJHSDVWH

UHQWHYRHWRS

0,00

6ODDWKHWEHGUDJRS

ZDDUPHHXEHJLQW

–3.000,00

6ODDWGHMDDUOLMNVH

EHWDOLQJRS

345.505,61

%HUHNHQWKHWEHGUDJ

GDWELMSHQVLRQHULQJRS

GHUHNHQLQJVWDDW

–87.556,47

%HUHNHQWGHFRQWDQWH

ZDDUGHYDQGH

NRRSNUDFKW)9ELMHHQ

LQIODWLHYDQ

10B.book Page 117 Wednesday, June 28, 2000 3:31 PM

118 8: Extra voorbeelden

Voorbeelden met cashflow

Wrap-aroundhypotheken

(HQZUDSDURXQGK\SRWKHHNLVHHQFRPELQDWLHYDQRSQLHXZILQDQFLHUHQ

YDQHHQK\SRWKHHNHQOHQHQRSEDVLVYDQYDVWJRHGHLJHQGRP*HZRRQOLMN

]LMQGHWZHHRQEHNHQGHJURRWKHGHQLQGHZUDSDURXQGK\SRWKHHNGH

QLHXZHEHWDOLQJHQKHWUHQGHPHQWYDQGHNUHGLHWJHYHU2PGLWSUREOHHP

RSWHORVVHQPRHWXJHEUXLNPDNHQYDQGH790WRHSDVVLQJqQGH

FDVKIORZWRHSDVVLQJ

Voorbeeld. 8PRHWQRJPDDQGHOLMNVHEHWDOLQJHQYDQGRHQRS

XZK\SRWKHHNYDQZDDUQRJHHQVDOGRYDQRSVWDDW8

ZLOWKLHUYDQJHEUXLNPDNHQHQHHQH[WUDOHQHQYRRUHHQDQGHUH

LQYHVWHULQJ8YLQGWLHPDQGGLHXNUHGLHWZLOYHUOHQHQWHJHQXZ

YDVWJRHGYHUPRJHQYRRUHHQEHGUDJYDQWHJHQRYHU

MDDU+RHKRRJ]LMQXZQLHXZHEHWDOLQJHQHQZDWLVKHWUHQGHPHQWGDWGH

NUHGLHWJHYHURSGH]HK\SRWKHHNNULMJW"

'HEHUHNHQLQJYDQGHEHWDOLQJLVHHQJHZRQH790EHWDOLQJEHUHNHQLQJ

ZDDUELMKHWQLHXZHEHGUDJDOV39ZRUGWJHEUXLNW

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

0,00

:LVWDOOHUHJLVWHUV

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

82.510,22

6ODDWEHGUDJYDQGHOHQLQJRS

ZDDURSXZQLHXZHOHQLQJLV

JHEDVHHUG

9,50

6ODDWGHUHQWHYRHWRS

0,00

6ODDWKHWODDWVWHVDOGRRS

180,00

6ODDWKHWWRWDDODDQWDO

PDDQGHOLMNVHEHWDOLQJHQRS

–861,59

%HUHNHQWGHQLHXZHEHWDOLQJ

10B.book Page 118 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 119

9RHUYHUYROJHQVGHFDVKIORZVLQGLHGHZUDSDURXQGK\SRWKHHNYDQXLWKHW

RRJSXQWYDQGHNUHGLHWJHYHUYROOHGLJYRRUVWHOOHQRPKHWUHQGHPHQWYDQ

GHNUHGLHWJHYHUWHEHUHNHQHQ

:DQQHHUXERYHQVWDDQGHFDVKIORZVJURHSHHUW]LHWXGDW

² ²

² 



 

² 

Toetsen: Display: Beschrijving:

CF0

–35.000,00

9RHUWLQDOVEHGUDJYDQ

GHOHQLQJLQ

CF1

107,59

9RHUWGHQHWWREHWDOLQJLQYRRU

GHHHUVWHPDDQGHQ

82,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

CF2

861,59

9RHUWGHQHWWREHWDOLQJLQYRRU

GHYROJHQGHPDDQGHQ

98,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

10,16

%HUHNHQWGHMDDUOLMNVH

RSEUHQJVW

10B.book Page 119 Wednesday, June 28, 2000 3:31 PM

120 8: Extra voorbeelden

Netto toekomstige waarde

'HQHWWRWRHNRPVWLJHZDDUGHNDQEHUHNHQGZRUGHQGRRUPHWGH790

WRHWVHQGHQHWWRKXLGLJHZDDUGH139LQKHWFDVKIORZGLDJUDPQDDU

UHFKWVWHVFKXLY HQ

Voorbeeld: Waarde van een fonds. 8KHEWGHDIJHORSHQWZHHMDDUGH

YROJHQGHVWRUWLQJHQJHGDDQLQHHQJHOGPDUNWIRQGVGDWRSEUHQJW

:DWLVKHWKXLGLJHVDOGRYDQXZUHNHQLQJ"

6WHOGH(LQGPRGXVLQ'UXNRS

DOVXGHBEGINLQGLFDWRU]LHW

Toetsen: Display: Beschrijving:

:LVWDOOHUHJLVWHUV

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU

MDDULQ

CF0

–12.000,00

9RHUWGHHHUVWHFDVKIORZLQ

CF1

0,00

9RHUWKHWEHGUDJLQYDQJURHS



2,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

CF2

–3.000,00

9RHUWKHWEHGUDJLQYDQJURHS



3,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

9,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

CF4

–7.500,00

9RHUWFDVKIORZJURHSLQ

10B.book Page 120 Wednesday, June 28, 2000 3:31 PM

8: Extra voorbeelden 121

3,00

9RHUWLQKRHYDDNGHEHWDOLQJ

YRRUNRPW

CF6

–2.000,00

9RHUWFDVKIORZJURHSLQ

8,80

6ODDWGHMDDUOLMNVHUHQWHYRHWRS

–29.203,14

%HUHNHQWGHQHWWRFRQWDQWH

ZDDUGH139GLHDXWRPDWLVFK

DOV39ZRUGWRSJHVODJHQ

24,00

6ODDWGHEHNHQGHZDDUGHQRS

0,00

34.800,58

%HUHNHQWGHQHWWRWRHNRPVWLJH

ZDDUGH

10B.book Page 121 Wednesday, June 28, 2000 3:31 PM

10B.book Page 122 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 123

Hulp, Batterijen en Service

+HZOHWW3DFNDUG]LHWKHWDOV]LMQWDDNRPEOLMYHQGHRQGHUVWHXQLQJWH

ELHGHQ8NXQWYDQRQV&DOFXODWRU6XSSRUW' HSDUWPH QWDQWZRRUGNULMJHQ

RSYUDJHQRYHUKHWJHEUXLNYDQGHFDOFXODWRU

/HHVHHUVW´$QWZRRUGHQRSGHPHHVWYRRUNRPHQGHYUDJHQµYRRUGDWX

PHWRQVFRQWDFWRSQHHPW2Q]HHUYDULQJLVGDWYHOHYDQRQ]HNODQWHQ

GH]HOIGHYUDJHQKHEEHQRYHURQ]HSURGXFWHQ$OVXJHHQDQWZRRUGRS

XZYUDJH QYLQGWNXQWX]LFKPHWRQVLQYHUELQGLQJVWHOOHQGRRUKHWDGUHV

RIWHOHIRRQQXPPHUWHJHEUXLNHQGDWRSGHELQQHQNDQWYDQKHW

DFKWHUEODGLVYHUPHOG

Antwoorden op de meest voorkomende

vragen

Q: :HUNWGHFDOFXODWRUJRHGRIGRHLN]HOILHWVYHUNHHUG"+RHNDQLN

YDVWVWHOOHQRIGHFDOFXODWRUJRHGZHUNW"

A: =LH´9DVWVWHOOHQRIGHFDOFXODWRUVHUYLFHQRGLJKHHIWµRSSDJLQD 

Q: ,QPLMQJHWDOOHQVWDDQNRPPD·VLQSODDWVYDQSXQWHQRPGHGHFLPDOHQ

DDQWHJHYHQ+RHNDQLNGHSXQWHQWHUXJNULMJHQ"

A: 'UXNRS SDJLQD 

Q: +RHNDQLNKHWDDQWDOGHFLPDOHQYHUDQGHUHQGDWGH+3 %,,LQGH

GLVSOD\WRRQW"

A: 'UXNRS JHYROJGGRRUKHWDDQWDOGHFLPDOHQGDWXZHQVW

SDJLQD 

10B.book Page 123 Wednesday, June 28, 2000 3:31 PM

124 A: Hulp, Batterijen en Service

Q: :DWEHWHNHQWHHQ´(µLQHHQ JHWDOELMYRRUE HHOG(²"

A: ([SRQHQ WYDQWLHQELMYRRUEHHOGï =LH

´:HWHQVFKDSSHOLMNHQRWDWLHµRSSDJLQD 

Q: :DDURP NULMJLNYH UNHHUGHDQWZRRUGHQRIGHPH OGLQJno SoLution ELM

KHWJHEUXLNYDQ790"

A: &RQWUROHHURIXELMYLHUYDQGHYLMI790ZDDUGHQHHQZDDUGHKHEW

LQJHYRHUGYRRUGDWXGHYLMIGHRSORVWRRNDOVppQYDQGHZDDUGHQQXOLV

9HUJHHWQLHWHHQQXOYRRU

RSWHVODDQDOVXHHQOHQLQJYROOHGLJDIORVW

+HWZLVVHQYDQDOOHUHJLVWHUV

YRRUGDWXXZEHNHQGHZDDUGHQ

LQYRHUWJHHIWKHW]HOIGHHIIHFW&RQWUROHHURIGHFDOFXODWRULQGHMXLVWH

EHWDOLQJVPRGXVVWDDW%HJLQRI(LQGPRGXVHQGDW3<5MXLVWLV

LQJHVWHOG

Q: +RHNDQLNKHWWHNHQYDQHHQJHWDOLQHHQOLMVWPHWFDVKIORZV

YHUDQGHUHQ"

A: 8PRHWGHLQJHYRHUGHFDVKIORZYHUDQGHUHQ=LH´&DVKIORZVEHNLMNHQ

HQYHUYDQJHQµRSSDJLQD 

Q: :DWEHWHNHQWPENDLQGHGLVSOD\"

A: (HQUHNHQNXQGLJHEHZHUNLQJZRUGWXLWJHYRHUG

Q: :DWEHWHNHQWINPUTLQGHGLVSOD\"

A:8KHEWRSGH WRHWVJHGUXNWSDJLQD 

Q: :DDURPLV,55<5JURWHUGDQLNYHUZDFKWWH"

A: 'LWLV,55SHUMDDU2PHHQ,55SHUSHU LRGHWHNULMJHQPRHWX,55

<5GHOHQ GRRU3<5

10B.book Page 124 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 125

Omgevingsfactoren

2PGLWSURGXFWEHWURXZEDDUWHODWHQZHUNHQPRHWXYHU PLMGHQGDWGH

FDOFXODWRUQDWZRUGWHQPRHWXGHYROJHQGHOLPLHWHQTXDWHPSHUDWXXUHQ

YRFKWLJKHLGLQDFKWQHPHQ

7HPSHUDWXXUELMJ HEUXLNWRW&WRW)

%HZDDUWHPSHUDWXXU²WRW&²WRW)

9RFKWLJKHLGELMJHEUXLNHQRSVODJUHODWLHYHYRFKWLJKHLGELM

PD[LPDDO&)

Geluidssterkte. ,QGHQRUPDOHKRXGLQJELMQRUPDDOJHEUXLNSHU,62

/S$G%

Voeding en Batterijen

'HFDOFXODWRUZRUGWJHYRHGGRRUWZHHYROWOLWKLXPNQRRSFHOEDWWHULMHQ

*HEUXLNHQNHOQLHXZHNQRRSFHOEDWWHULMHQDOVXGHEDWWHULMHQYHUYDQJW

%HLGHEDWWHULMHQPRHWHQWHJHOLMNYHU YDQJHQZRUGHQ

*HEUXLNJHHQRSODDGEDUHEDWWHULMHQ

Batterij-indicator

$OVGHLQGLFDWRU ]LFKWEDDULVEHWHNHQWGLWGDWXGHEDWWHULMHQ]R

VSRHGLJPRJHOLMNPRHWYHUYDQJHQ'HLQGLFDWRUIOLNNHUWDOVGH

VWURRPVWHUNWHWHODDJZRUGW

$OVGHEDWWHULMLQGLFDWRUDDQJDDWHQGHGLVSOD\]ZDNNHUZRUGWYHUOLFKWNDQ

KHW]LMQGDWXJ HJHYHQVNZLMWUDDNW$OV JHJHYHQVYHUORUHQJDDQWHQJHYROJH

YDQWHODJHVWURRPVWHUNWH]LHWXGHPHOGLQJ

All Clear 

Batterijspecificaties

8Z+3FDOFXODWRUJHEUXLNWWZHHOLWKLXPEDWWHULMHQ&5

10B.book Page 125 Wednesday, June 28, 2000 3:31 PM

126 A: Hulp, Batterijen en Service

Batterijen plaatsen

 =RUJGDWXWZHHQLHXZH&5EDWWHULMHQKHEW5DDNEDWWHULMHQ

HQNHODDQGHUDQGDDQ9HHJHONHEDWWHULMVFKRRQP HWHHQQLHW

SOXL]HQGHGRHNRPYXLOHQYHWWHYHUZLMGHUHQ

 &RQWUROHHURIGHFDOFXODWRUXLWVWDDW8YHUOLHVWGHLQKR XGYDQKHW

JHKHXJHQDOVXGHEDWWHULMHQYHUYDQJWVFKULMIGXVGHJHJHYHQVRSGLH

XRSJHVODJHQKH EWHQQRGLJKHEWYRRUODWHUJ HEUXLN

 'UDDLGHFDOFXODWRURPHQYHUZLMGHUGHNOHSYDQGHEDWWHULMKR XGHU

Toegang tot de batterijhouder

 9HUZLMGHUEHLGHEDWWHULMHQ

 3ODDWVGHQLHXZHEDWWHULMHQHQFRQWUROHHU RIKHWSRV LWLHIWHNHQ

RSHONHEDWWHULMQDDUEXLWHQZLMVW

 3ODDWVGHNOHSYDQGHEDWWHULMKRXGHUWHUXJ

 'UXNRS



$OVGHFDOFXODWRUQLHWDDQJDDWYROJGDQGHSURFHGXUHVLQGHYROJHQGH

SDUDJUDDI

Let op!

Gevaar voor explosie indien batterij niet correct

wordt vervangen.

Vervang de batterij enkel met een zelfde of

gelijksoortig type, zoals aangeraden door de

fabrikant. Gooi de gebruikte batterijen weg volgens

de instructies van de fabrikant.

Beschadig de batterijen niet, prik er niet in en gooi

batterijen niet in het vuur. Batterijen kunnen

openbarsten of ontploffen waardoor gevaarlijke

chemische stoffen vrij kunnen komen.

Gebruik geen nieuwe en oude batterijen of batterijen

van verschillende types door elkaar.

10B.book Page 126 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 127

Vaststellen of de calculator service nodig heeft

*HEUXLNGH]HULFKWOLMQHQRPWHEHSDOHQRIGHFDOFXODWRUVHUYLFHQRGLJ

KHHIW$OVGHSURFHGXUHVEHYHVWLJHQGDWGHFDOFXODWRUQLHWQDDUEHKRUHQ

ZHUNWOHHVGDQGHSDUDJUDDI´$OVGHFDOFXODWRUVHUYLFHQRGLJKHHIWµRS

SDJLQD 

De calculator is niet aan te krijgen (er verschijnt niets in de

display):

'H]HVLWXDWLHEHWHNHQWPHHVWDOGDWGHEDWWHULMHQOHHJ]LMQ3ODDWV

QLHXZHEDWWHULMHQ

$OVGHFDOFXODWRUQRJVWHHGVQLHWDDQWHNULMJHQLVDOVXRS

GUXNW

 VWHOGHFDOFXODWRURSQLHXZLQ]LHYHUGHUHQLQGLHQQRGLJ

 :LVKHWJHKHXJHQ]LHYHUGHU

'HPHOGLQJ

All Clear ]RXQXPRHWHQYHUVFKLMQHQ$OVGLWQLHWKHW

JHYDOLVGDQLVVHUYLFHQRGLJ

De calculator opnieuw instellen

 'UDDLGHFDOFXODWRURPHQYHUZLMGHUGHNOHSYDQGH

EDWWHULMKRXGHU

 'UXNKHWXLWHLQGHYDQHHQSDSHUFOLSLQKHWNOHLQHURQGHJDW

WXVVHQGHEDWWHULMHQ'UXNGHFOLS]RYHUPRJHOLMNLQKHWJDW

+RXGH]HppQVHFRQGHLQJHGUXNWHQYHUZLMGHUGDQGHFOLS

 'UXNRS



 $OVGHFDOFXODWRUQRJVWHHGVQLHWUHDJHHUWZLVGDQKHWJHKHXJ HQ

]LHYHUGHUHQKHUKDDOVWDSSHQWRWQRJHHQNHHU

Het geheugen van de calculator wissen

 +RXGGH WRHWVLQJHGUXNW

 +RXGYHUYROJHQV]RZHOGH

DOVGH WRHWVLQJHGUXNW

 /DDWGHGULHWRHWVHQORV

+HWJHKHXJHQLVJHZLVWHQGHPHOGLQJ

All Clear]RXQX]LFKWEDDU

PRHWHQ]LMQ

10B.book Page 127 Wednesday, June 28, 2000 3:31 PM

128 A: Hulp, Batterijen en Service

De calculator reageert niet op op het aanslaan van toetsen (er

gebeurt niets als u op de toetsen drukt):

 6WHOGHFDOFXODWRURSQLHXZLQzie bovenHQLQGLHQQRGLJ

 ZLVKHWJHKHXJHQ

zie boven

'HPHOGLQJ

All Clear ]RXQXPRHWHQYHUVFKLMQHQ$OVGLWQLHWKHW

JHYDOLVGDQLVVHUYLFHQRGLJ

De calculator reageert wel op toetsaanslagen maar u

vermoedt dat hij toch niet werkt zoals het hoort:

 +HWLVPRJHOLMNGDWXHHQIRXWKHEWJHPDDNWELMKHWEHGLHQHQ

YDQGHFDOFXODWRU+HUOHHVGHWRHSDVVHOLMNHGHOHQYDQGH

KDQGOHLGLQJHQFRQWUROHHU´$QWZRRUGHQRSGHPHHVW

YRRUNRPHQGHYUDJHQµRSSDJLQD 

 1HHPFRQWDFWRSPHWKHW&DOFXODWRU6XSSRUW'HSDUWPHQW+HW

DGUHVHQWHOHIRRQQXPPHUVWDDQDDQGHELQQHQ]LMGHYDQKHW

DFKWHUEODG

Beperkt garantiebewijs voor één jaar

Wat onder de garantie valt

+HZOHWW3DFNDUGJHHIWJDUDQWLHRSGHFDOFXODWRUPHWXLW]RQGHULQJYDQGH

EDWWHULMHQRIVFKDGHYHURRU]DDNWGRRUGHEDWWHULMHQ WHQDDQ]LHQYDQ

PDWHULDDOGHIHFWHQHQRQWRHUHLNHQGYDNPDQVFKDSJHGXUHQGHppQMDDUQDGHGDWXPYDQ

RRUVSURQNHOLMNHDDQNRRS$OVXGHFDOFXODWRUYHUNRRSWRIZHJJHHIWJDDWGH

JDUDQWLHDXWRPDWLVFKRYHURSGHQLHXZHHLJHQDDUHQ EOLMIWJHOGLJ

JHGXUHQGHGHRRUVSURQ NHOLMNHSHULRGHYDQppQMDDU*HGXUHQGHGH

JDUDQWLHWHUPLMQNXQWXHHQSURGXFWGDWPDQNHPHQWHQYHUWRR QWGRRURQV

NRVWHORRVODWHQUHSDUHUHQRIYHUYDQJHQRSYRRUZDDUGHGDWXKHW

EHWUHIIHQGHSURGXFWYROGRHQGHJHI UDQNHHUGDDQHHQVHUYLFHGLHQVWYDQ

+HZOHWW3DFNDUGUHWRXUQHHUW9HUYDQJLQJNDQJHVFKLHGHQGR RUHHQ

QLHXZHURIJHOLMNZDDUGLJPRGHORIHHQPR GHOPHWEHWHUHIXQFWLRQDOLWHLW

'LWJDUDQWLHEHZLMVJHHI WXEHSDDOGHZHWWHOLMNHUHFKWHQ7HYHQVNXQWX

EHSDDOGHUHFKWHQKHEEHQ GLHSHUODQGHQ]HOIVELQ QHQHHQODQGNXQQHQ

YHUVFKLOOHQ

10B.book Page 128 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 129

Wat niet onder de garantie valt

%DWWHULMHQHQGRRUEDWWHULMHQYHURRU]DDNWHV FKDGHZRUGHQQLHWGRRUGH

+HZOHWW3DFNDUGJDU DQWLHJHGHNW5DDGSOHHJXZOHYHUDQFLHURYHUJDUDQWLH

RSEDWWHULMHQHQZDWEHWUHIWOHNNDJHV

'LWJDUDQWLHEHZLMVLVQLHWJ HOGLJZDQQHHUKHWSURGXFWEHVFKDGLJGLVGRRU 

HHQRQJHYDORIRQGHVNXQGLJJH EUXLNWRIWHQJHYROJHYDQRQGHUKRXGRI

DDQSDVVLQJGRRUHHQQLHWGR RU+HZOHWW3DFNDUGHUNHQGHVHUYLFHGLHQVW

(UZRUGWJHHQ DQGHUHVSHFLDOHJDUDQWLHYHUVWUHNW5HSDUDWLHRIYHUYDQJLQJ

YDQHHQSURGXFWLVXLWVOXLWHQGXZHLJHQYHUDQWZRRUGHOLMNKHLG$OOH

DQGHUHJHwPSOLFHHUGHJDUDQWLHVEHWUHIIHQGHYHUNRRSEDDUKHLGHQ

FRQGLWLHYDQKHWDSSDUDDWJHOGHQXLWVOXLWHQGYRRUGH

JDUDQWLHSHULRGHYDQGLWVFKULIWHOLMNHEHZLMV'RRUGDWLQ VRPPLJH

ODQGHQEHSHUNLQJHQDDQJDDQGHGHGXXUYDQGHJHwP SOLFHHUGHJDUDQ WLH

QLHWWRHJHVWDDQ]LMQKRHIWERYHQVWDDQGHEHSHUNLQJQLHWYRRUXWHJHOGHQ

,QJHHQJHYDONDQ+HZOHWW3DFNDUG1HGHUODQG%9

YHUDQWZRRUGHOLMNZRUGHQJHVWHOGYRRUELMNRPHQGHVFKDGH'RR UGDW

LQVRPPLJHODQGHQEHSHUNLQJRIXLWVOXLWLQJYDQGHJDUDQWLHYRRU

LQFLGHQWHOHRIELMNRPHQGHVFKDGHQLHWLVWRHJ HVWDDQKRHIWERYHQVWDDQGH

XLWVOXLWLQJRIEHSHUNLQJQLHWYRRUXWHJHOGHQ 

3URGXFWHQZRUGHQYHUNRFKWRSEDVLVYDQVSHFLILFDWLHVGLHYDQWRHSDVVLQJ

ZDUHQRSKHWWLMGVWLSYDQSURGXFWLH+HZOHWW3DFNDUGLVQLHWYHU SOLFKW

UHHGVYHUNRFKWHSURGXFWHQDDQWHSDVVHQRIWHPRGHUQLVHUHQ

Klantentransacties in het Verenigd Koninkrijk

'H]HJDUDQWLHLVQLHWYDQWRHSDVVLQJRSNODQWHQWUDQVDFWLHVHQKHHIWJHHQ

LQYORHGRSGHJURQGZHWWHOLMNHUHFKWHQYDQHHQFRQVXPHQW0HW

EHWUHNNLQJWRWGHUJHOLMNHWUDQVDFWLHVZRUGHQGHUHFKWHQHQYHUSOLFKWLQJHQ

YDQNRSHUHQYHUNRSHUELMZHWEHSDDOG

10B.book Page 129 Wednesday, June 28, 2000 3:31 PM

130 A: Hulp, Batterijen en Service

Als de calculator service nodig heeft

+HZOHWW3DFNDUGKHHIWVHUYLFHGLHQVWHQLQYHOHODQGHQ'H]HGLHQVWHQ

UHSDUHUHQFDOFXODWRUVRIYHUYDQJHQGH]HGRRUKHW]HOIGHPRGHORIGRRU

HHQPRGHOPHWHHQKRJHUHZDDUGHRQJHDFKWGHJDUDQWLHEHSDOLQJHQ1D

KHWYHUVWULMNHQYDQGHJDUDQWLHSHULRGHZRUGHQYRRUVHUYLFHNRVWHQLQ

UHNHQLQJJ HEUDFKW*HZRRQOLMNJHVFKLHGWRQGHUKRXGDDQHQWHUXJ]HQGLQJ

YDQFDOFXODWRUVELQQHQYLMIZHUNGDJHQ

Service-adressen

In de Verenigde Staten:6WXXUGHFDOFXODWRUQDDUHHQHUNHQGH+3

VHUYLFHGLHQVW]LHELQQHQ]LMGHRPVODJ

In Europa:1HHPFRQWDFWRSPHW+HZOHWW3DFNDUGLQ1HGHUODQGRI

%HOJLs]LHELQQHQ]LMGHRPVODJKHW(XURSHVHKRRIGNZDUWLHUYDQ

+HZOHWW3DFNDUGRIPHWXZGHDOHUYRRUDGUHVVHQYDQGH

GLFKWVWELM]LMQGHVHUYLFHGLHQVW9HUVWXXUGHFDOFXODWRUQLHWYRRURQGHUKRXG

]RQGHUHHUVWFRQWDFWRSJHQRPHQWHKHEEHQPHWHHQ+HZOHWW3DFNDUGYHVWLJLQJ

*DQDDUKWWSZZZKSFRPFDOFXODWRUVYRRUHHQOLMVWYDQ

VHUYLFHGLHQVWHQLQ(XURSD

In andere landen:1HHPFRQWDFWRSPHWKHW+HZOHWW3DFNDUG

YHUNRRSNDQWRRURIPHWXZGHDOHURIVFKULMIQDDUHHQHUNHQGH+3

VHUYLFHGLHQVW]LHELQQHQ]LMGHRPVODJYRRUDGUHVVHQYDQDQGHUH

VHUYLFHGLHQVWHQ$OVSODDWVHOLMNJHHQVHUYLFHEHVFKLNEDDULVNXQWXGH

FDOFXODWRUYRRUUHSDUDWLHVYHUVWXUHQQDDUHHQHUNHQGH+3

VHUYLFHGLHQVW

9HU]HQGLQJUHJHOLQJYDQKHULPSRUWHQGRXDQHNRVWHQ]LMQXZHLJHQ

YHUDQWZRRUGHOLMNKHLG

Servicekosten

9RRUVHUYLFHYHUOHQLQJEXLWHQGHJDUDQWLHWHUPLMQEHVWDDQYDVWHWDULHYHQ

+HWVHUYLFHFHQWUXP]LHELQQHQ]LMGHDFKWHUEODGNDQXYHUWHOOHQZDWGH

NRVWHQ]LMQ'H]HNRVWHQ]LMQRQGHUKHYLJDDQGHSODDWVHOLMNHEHSDOLQJHQ

YRRUYHUNRRSVEHODVWLQJHQ%7:DOVGH]HYDQWRHSDVVLQJ]LMQ

'HYDVWHUHSDUDWLHNRVWHQ]LMQQLHWYDQWRHSDVVLQJDOVGHFDOFXODWRUGRRU

RQJHYDORIRQGHVNXQGLJJHEUXLNLVEHVFKDGLJG,QGH]HJHYDOOHQZRUGW

KHWWDULHIEHSDDOGRSJURQGYDQEHVWHGHWLMGHQNRVWHQYRRUPDWHULDDO

10B.book Page 130 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 131

Verzendinstructies

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10B.book Page 131 Wednesday, June 28, 2000 3:31 PM

132 A: Hulp, Batterijen en Service

Verdere informatie

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10B.book Page 132 Wednesday, June 28, 2000 3:31 PM

A: Hulp, Batterijen en Service 133

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134 A: Hulp, Batterijen en Service

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10B.book Page 134 Wednesday, June 28, 2000 3:31 PM

B: Nog meer berekeningen 135

Nog meer berekeningen

IRR/YR Berekeningen

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Mogelijke resultaten bij het berekenen van IRR/YR

'HPRJHOLMNHUHVXOWDWHQYDQHHQ,55<5EHUHNHQLQJ]LMQ

Geval 1.'HFDOFXODWRUWRRQWHHQSRVLWLHYHRSORVVLQJ'LWLVGHHQLJH

SRVLWLHYHRSORVVLQJ(UNXQQHQHFKWHUppQRIPHHUQHJDWLHYH

XLWNRPVWHQEHVWDDQ

Geval 2.'HFDOFXODWRUYLQGWHHQQHJDWLHYHRSORVVLQJPDDUHHQ

HQNHOYRXGLJHSRVLWLHYHRSORVVLQJEHVWDDWRRN8]LHW

Pos Irr Also8

NULMJWGHQHJDWLHYHRSORVVLQJWH]LHQGRRURS

WHGUXNNHQRPGH

PHOGLQJWHZLVVHQ8YLQGWGHSRVLWLHYHRSORVVLQJGRRUHHQVFKDWWLQJ

LQWHYRHUHQ=LH´(HQVFKDWWLQJLQYRHUHQYRRU,55<5µ

KLHURQGHU(UNXQQHQRRNQRJH[WUDQHJDWLHYHXLWNRPVWHQ]LMQ

Geval 3.'HFDOFXODWRUWRRQWHHQQHJDWLHIDQWZRRUGHQJHHQ

PHOGLQJ'LWLVGHHQLJHRSORVVLQJ

10B.book Page 135 Wednesday, June 28, 2000 3:31 PM

136 B: Nog meer berekeningen

Geval 4.'HFDOFXODWRUWRRQWGHPHOGLQJNot Found'LWJHHIWDDQ

GDWGHEHUHNHQLQJ]HHULQJHZLNNHOGLV(UNDQPHHUGDQppQSRVLWLHYH

RIQHJDWLHYHRSORVVLQJ]LMQRIHUNDQJHHQRSORVVLQJ]LMQ2PPHWGH

EHUHNHQLQJYHUGHUWHJDDQPRHWXHHQEHQDGHULQJRSVODDQ]LH

KLHURQGHU

Geval 5.'HFDOFXODWRUWRRQWGHPHOGLQJNo Solution(ULVJHHQ

RSORVVLQJ'H]HVLWXDWLHNDQYRRUNRPHQDOVHUHHQIRXWLVJHPDDNW

ELMYRRUEHHOGELMKHWLQYRHUHQYDQGHFDVKIORZV(HQYDDN

YRRUNRPHQGHIRXWGLHGH]HPHOGLQJWRWUHVXOWDDWKHHIWLVKHW

SODDWVHQYDQKHWYHUNHHUGHWHNHQYRRUHHQFDVKIORZ(HQFRUUHFWH

VHULHFDVKIORZVYRRUHHQ,55<5EHUHNHQLQJPRHWWHQPLQVWHppQ

SRVLWLHYHHQppQQHJDWLHYHFDVKIORZKHEEHQ

IRR/YR stoppen en opnieuw beginnen

+HW]RHNHQQDDU,55<5NDQUHODWLHIODQJGXUHQ8NXQWGHEHUHNHQLQJ

RSLHGHUPRPHQWVWRSSHQGRRURSGH

WRHWVWHGUXNNHQ8]LHWGDQGH

PHOGLQJ

IntErruPtEd$OVXQXRS GUXNW]LHWXGHEHQDGHULQJYDQ

,55<5YDQGLWRJHQEOLN8NXQWGHEHUHNHQLQJRSQLHXZODWHQEHJLQQHQ

GRRUKHWYROJHQGHWHGRHQ

'UXNRS WHUZLMOGHKXLGLJHEHQDGHULQJLQGHGLVSOD\

VWDDWZHHUJHJHYHQ+LHUGRRUZRUGWGHEHUHNHQLQJZHHUEHJRQQHQ

YDQDIKHWSXQWZDDUGH]HZHUGDIJHEURNHQ

+HWRSVODDQYDQHHQVFKDWWLQJYRRU,55<5VWDDWKLHURQGHU

EHVFKUHYHQ

Een schatting invoeren voor IRR/YR

8YRHUWHHQVFKDWWLQJLQGRRUHHQEHQDGHULQJYDQ,55<5LQWHYRHUHQ

HQYHUYROJHQVRS

WHGUXNNHQ8NXQWRSGHYROJHQGH

PRPHQWHQHHQVFKDWWLQJYDQ,55<5LQYRHUHQ

9yyUGHEHUHNHQLQJ(HQUHGHOLMNQDXZNHXULJHVFKDWWLQJNDQGH

EHQRGLJGHWLMGYRRUKHWEHUHNHQHQYDQHHQRSORVVLQJYHUNRUWHQHQ

GHNDQVGDWGHFDOFXODWRUHHQRQJHZHQVWHQHJDWLHYHRSORVVLQJYLQGW

YHUPLQGHUHQ

1DGDWXGHEHUHNHQLQJKHEWRQGHUEURNHQ

1DGDWGHFDOFXODWRULVJHVWRSWGRRUppQYDQGHKLHUYRRUJHQRHPGH

UHGHQHQ9RRUGHJHYDOOHQHQ]XOOHQHFKWHUJHHQDQGHUH

RSORVVLQJHQZRUGHQJHYRQGHQ

10B.book Page 136 Wednesday, June 28, 2000 3:31 PM

B: Nog meer berekeningen 137

%LMKHWEHUHNHQHQYDQ,55<5PHWEHKXOSYDQHHQVFKDWWLQJVWRSWGH

EHUHNHQLQJZDQQHHUHHQRSORVVLQJLVJHYRQGHQ(UNXQQHQHFKWHUQRJ

PHHUSRVLWLHYHRIQHJDWLHYHRSORVVLQJHQ]LMQRIKHOHPDDOJHHQRSORVVLQJ

8NXQWQDDUHHQDQGHUHRSORVVLQJEOLMYHQ]RHNHQGRRUGHEHUHNHQLQJWH

VWRSSHQHQHHQDQGHUHVFKDWWLQJLQWHYRHUHQ

+HWEHUHNHQHQYDQ139YRRUYHUVFKLOOHQGHUHQWHYRHWHQLVHHQPDQLHU

RPHHQJRHGHVFKDWWLQJYRRU,55<5WHNULMJHQ$DQJH]LHQ,55<5 GH

UHQWHYRHWLVZDDUELM139JHOLMNDDQQXOLVLVGHEHVWHEHQDGHULQJYDQ

,55<5GHUHQWHYRHWZDDUYRRUGHZDDUGHYDQ139QXOKHWGLFKWVW

EHQDGHUW

Gevolgen van het gebruik van

– voor het

verbeteren van gegevens

'H+3%,,VODDWVWDWLVWLVFKHJHWDOOHQRS´JHDFFXPXOHHUGHµZLM]HRS

1LHWLHGHUJHWDOGDWXLQYRHUWZRUGWRSJHVODJHQPDDUHUZRUGHQ

WXVVHQWLMGVHEHUHNHQLQJHQXLWJHYRHUGDOVXRSGH

WRHWVGUXNW'H

WRHWVYRHUWGHWHJHQRYHUJHVWHOGHEHUHNHQLQJHQXLWRPHHQJHWDORI

HHQJHWDOOHQSDDUZHUNHOLMNWHYHUZLMGHUHQXLWGHRSJHVODJHQUHVXOWDWHQ

%LMKHWYHUEHWHUHQYDQVWDWLVWLVFKHJHJHYHQVZRUGHQDIURQGLQJVIRXWHQ

GLHELMWXVVHQWLMGVHEHUHNHQLQJHQYRRUNRPHQWLMGHQVEHZHUNLQJHQGLHPHW

]LMQXLWJHYRHUGQLHWGRRU YHUZLMGHUG+LHUGRRUNXQQHQ

UHVXOWDWHQYRRUYHUEHWHUGHJHJHYHQVDIZLMNHQYDQJHJHYHQVGLHLQJHYRHUG

]LMQ]RQGHUGDW

JHEUXLNWZHUG+HWYHUVFKLOLVHFKWHUQLHWYDQ

EHODQJWHQ]LMGHRQMXLVWHJHJHYHQV]HHUJURRW]LMQWHQRS]LFKWHYDQGH

MXLVWHJHJHYHQVLQGLWJHYDOLVKHWZDDUVFKLMQOLMNEHWHURPVWDWLVWLVFKH

UHJLVWHUVWHZLVVHQHQGHJHJHYHQVRSQLHXZLQWHYRHUHQ

Getallenbereik

'HJURRWVWHSRVLWLHYHHQQHJDWLHYHJHWDOOHQZDDUPHHGHFDOFXODWRUZHUNW

]LMQï

GHNOHLQVWHSRVLWLHYHHQQHJDWLHYHJHWDOOHQ

]LMQï

(HQXQGHUIORZJHHIWNRUWUFLOZHHUJHYROJGGRRUQXO

5DDGSOHHJGHPHOGLQJHQ

OFLOHQUFLOLQ´0HOGLQJHQµLQKHW

KLHUQDYROJHQGHDDQKDQJVHO

10B.book Page 137 Wednesday, June 28, 2000 3:31 PM

138 B: Nog meer berekeningen

Formules

Berekening van marge en brutowinst



Time Value of Money (TVM)

%HWDOLQJVPRGXVIDFWRU6 YRRUGH(LQGPRGXVYRRUGH%HJLQPRGXV

0$5

35& .267

–

35&









×=

35& .267

–

.267









×=

L

,<5

3<5



0 PV



L

S×



---------------+





307



L









N–

–

L



--------

-------------------------------------







××

FV+1

L



--------





N–

10B.book Page 138 Wednesday, June 28, 2000 3:31 PM

B: Nog meer berekeningen 139

Amortisatie

%$/LVLQHHUVWHLQVWDQWLHJHOLMNDDQ39DIJHURQGQDDUGHKXLGLJH

LQVWHOOLQJYDQGHGLVSOD\

307LVLQHHUVWHLQVWDQWLHJHOLMNDDQ307DIJHURQGQDDUGHKXLGLJH

LQVWHOOLQJYDQGHGLVSOD\

9RRULHGHUHJHDPRUWLVHHUGHDIEHWDOLQJ

Rentevoet conversies

,17 JHFXPXOHHUGHUHQWH

351 JHFXPXOHHUGHKRRIGVRP

L SHULRGLHNHUHQWHYRHW

,17

%$/ïL,17·ZRUGWDIJHURQGQDDUGHKXLGLJHLQVWHOOLQJ

YDQGHGLVSOD\,17· YRRUSHULRGHLQGH%HJLQPRGXV

,17 ,17PHWKHWWHNHQYDQ307

351 307,17 

%$/

351

,17

,17

351

351

,<5

3<5 

×⁄

-----------------------------=

())

120

 3<5

⁄×

-----------------------------+





PYR⁄



–







×=

10B.book Page 139 Wednesday, June 28, 2000 3:31 PM

140 B: Nog meer berekeningen

Cashflowberekeningen

$OV139 LVGHRSORVVLQJYRRULKHWSHULRGLHNHLQWHUQHUHQGHPHQW

L SHULRGLHNHUHQWHYRHW

M KHWQXPPHUYDQGHFDVKIORZJURHS

KHWEHGUDJYDQGHFDVKIORZYRRUJURHSM

DDQWDONHUHQGDWGHFDVKIORZYRRUNRPWYRRUJURHSM

N KHWQXPPHUYDQGHODDWVWHJURHSYDQFDVKIORZV

1M WRWDDODDQWDOFDVKIORZVYRRUDIJDDQGDDQGHJURHSM

1 lj<≤

∑

NPV CF

j 1=

∑

L



--------+





–

L



--------

-------------------------------------







× 1

L



--------





–

10B.book Page 140 Wednesday, June 28, 2000 3:31 PM

B: Nog meer berekeningen 141

Statistiek

 



[

∑

-------=

∑

-------=

[

∑

----------=

[

∑

[

∑

()

--------------

–

Q 

–

-------------------------------

∑

()

--------------

–

Q 

–

------------------------------

σx

[

∑

[

∑

()

--------------

–

-------------------------------

σy

∑

()

--------------

–

------------------------------

∑

---------------

–

∑

()

--------------

–





∑

()

--------------

–





----------------------------------------------------------------------------

∑

---------------

–

∑

()

--------------

–

--------------------------------

bymx–=

yb–

-----------

= y

mx b+=

10B.book Page 141 Wednesday, June 28, 2000 3:31 PM

10B.book Page 142 Wednesday, June 28, 2000 3:31 PM

C: Meldingen 143

Meldingen

'UXNRS RI RPHHQPHOGLQJYDQGHGLVSOD\WHZLVVHQ

All Clear

+HWEOLMYHQGJHKHXJ HQ LVJ HZLVWSD JLQD 

COPR HP2000

&RS\ULJK WE HULFKW

Interrupted

(HQ,55<5,<5RIDPR UWLVD WLHEHUHNHQLQJZHUGRQ GHUE UR NHQGRR U

KHWLQGUXNNHQYDQ



No Solution

*HHQ2SORVVLQJ(UEHVWDDWJHHQRSORVVLQJYRRUGHLQJHYRHUGH

ZDDUGHQSDJLQD 

Not Found

(UNDQHHQR SOR VV LQJE HV WDDQYRRU, 55<5R I ,<5$OVXSUREHHUWRP

,<5RSWHORVVHQLVK HWPRJH OLMNGDWXGHEHUH NHQLQJNXQWXLWYR HU HQPHW

JHEUXLNYDQ,55<5$OV XHHQ,55<5 E HU HNHQLQJSUR E HHUWR SWH

ORVVHQ]LHGDQ S DJLQD 

OFLO

2YHUIORZ+HWUHVXOWDDWYDQHHQEHU HNHQLQJLVWHJU R RWYRRUGH

FDOFXODWRURPP HHWHNXQQ HQ ZHUNHQ'HPHOGLQ JZRUGWJHGXUHQ GHHHQ

NRUWPR PHQ WJ HWR RQ GHQYHUYROJHQ V]LH WXKHWUHVXOWDDWYDQGHRYHUIORZ

('HRYHUI ORZPHOGLQJ]LHWXRR NDOVKH WUHVXOWDDW

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10B.book Page 143 Wednesday, June 28, 2000 3:31 PM

144 C: Meldingen

Pos Irr Also

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10B.book Page 144 Wednesday, June 28, 2000 3:31 PM

Index 145

Index

7RHWVHQGLHKLHUQLHWZHHUJHJHYHQ]LMQ

NXQWXWHUXJYLQGHQLQGHDOIDEHWLVFKH

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Speciale tekens

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10B.book Page 145 Wednesday, June 28, 2000 3:31 PM

146 Index

%HWDOLQJ

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10B.book Page 146 Wednesday, June 28, 2000 3:31 PM

Index 147

*HWDOQRWDWLH

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10B.book Page 147 Wednesday, June 28, 2000 3:31 PM

148 Index





N 

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3HULRGLHNHUHQWH

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3RSXODWLHVWDQGDDUGGHYLDWLH

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HQEHWDOLQJVSHULRGHV

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10B.book Page 148 Wednesday, June 28, 2000 3:31 PM

Index 149

6HUYLFH 

(XURSD



86$

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DQGHUHODQGHQ

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VQLMSXQWPHWGH\DV

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6RPPDWLHVWDWLVWLHNHQ

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VWHHNSURHI

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STAT , 

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EHQDGHULQJ

, 

JHPLGGHOGH

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YHUZDFKWLQJHQ

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6WDWLVWLHNHQPHWppQ YDULDEHOH

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6WHHNSURHIVWDQGDDUGGHYLDWLH



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7HUPHQHQFRQGLWLHV

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, 

790

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9HHOYRRUNRPHQGHYUDJHQ

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9HUGHUHLQIRUPDWLH

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9HUGLVFRQWHHUGHK\SRWKHNHQ

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9HUGLVFRQWHUHQYDQFDVKIORZV

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9HUNRRSSULMVYDVWVWHOOHQ

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9HUZDFKWLQJHQ

, 

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9LHUNDQWVZRUWHO

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10B.book Page 149 Wednesday, June 28, 2000 3:31 PM

150 Index

:HWHQVFKDSS HOLMNHQRWDWLH 

:LVVHQ

GLVSOD\

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JHKHXJHQ

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790

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:UDSDURXQGK\SRWKHNHQ







10B.book Page 150 Wednesday, June 28, 2000 3:31 PM

HP 10BII Handleiding

Merk: HP

Model: 10BII

Type: Handleiding

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