hp 10BII Zakelijke Calculator

hp 10BII Zakelijke Calculator Gebruikershandboek

Editie 1 HP artikelnummer F1902-90013

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

© Copyright 1988, 1989, 2001, 2004 Hewlett-Packard Development 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

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

Mei 2003

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

Welkom bij de HP 10BII 8Z+3%,,LVHHQYRRUEHHOGYDQGHEXLWHQJHZRRQKRJHNZDOLWHLWHQGH ELM]RQGHUJURWHDDQGDFKWYRRUGHWDLOVHQSURGXFWLHGLHDOPHHUGDQMDDU KHWNHQPHUN]LMQYDQ+HZOHWW3DFNDUG+HZOHWW3DFNDUGVWDDWDFKWHUGH]H FDOFXODWRU³ZLMELHGHQRYHUGHJHKHOHZHUHOGVHUYLFHHQH[SHUWLVHRPKHW JHEUXLNHUYDQWHRQGHUVWHXQHQ]LHELQQHQNDQWRPVODJ

Hewlett-Packard kwaliteit 2Q]HFDOFXODWRUV]LMQJHPDDNWRPXLWWHEOLQNHQLQGXXU]DDPKHLGHQ JHEUXLNVJHPDN n 'H]HFDOFXODWRULV]RRQWZRUSHQGDWVFKRNNHQWULOOLQJHQYHUYXLOLQJ VPRJR]RQ WHPSHUDWXXUVZLVVHOLQJHQHQYHUDQGHULQJHQLQ YRFKWLJKHLGGLHWLMGHQVKHWGDJHOLMNVHZHUNYRRUNRPHQGRRUVWDDQ NXQQHQZRUGHQ n 'HFDOFXODWRUHQGHKDQGOHLGLQJ]LMQJHWHVWRS JHEUXLNVYULHQGHOLMNKHLG:LMKHEEHQYHHOYRRUEHHOGHQDDQGH KDQGOHLGLQJWRHJHYRHJGRPGHPRJHOLMNKHGHQYDQGH]HFDOFXODWRUWH EHQDGUXNNHQ'HQLHXZVWHPDWHULDOHQHQEOLMYHQGHLQJHJRWHQWHNHQV RSGHWRHWVHQ]RUJHQYRRUHHQGXXU]DDPWRHWVHQERUGGDWSOH]LHULJ DDQYRHOWELMJHEUXLN n /DDJYHUPRJHQHOHNWURQLFDHQKHWJHDYDQFHHUGHV\VWHHPYRRU HQHUJLHEHKHHUYHUKRRJWGHOHYHQVGXXUYDQGHEDWWHULMHQ n 'HPLFURSURFHVVRULVJHRSWLPDOLVHHUGRPRSVQHOOHHQEHWURXZEDUH ZLM]HEHUHNHQLQJHQXLWWHNXQQHQYRHUHQZDDUELMLQWHUQFLMIHUV JHEUXLNWZRUGHQRPQDXZNHXULJHUHVXOWDWHQWHEHKDOHQ

Welkom bij de HP 10BII

3


n 1DXLWJHEUHLGRQGHU]RHNLVHUHHQRQWZHUSJHNRPHQGDWGHVOHFKWH

LQYORHGHQYDQVWDWLVFKHHOHNWULFLWHLWPLQLPDOLVHHUWHHQSRWHQWLsOH EURQYDQIRXWHQHQJHJHYHQVYHUOLHVLQFDOFXODWRUV

Eigenschappen 'HHLJHQVFKDSSHQYDQGH+3%,,HQGHKDQGOHLGLQJJHYHQGHZHQVHQ YDQYHOHNODQWHQZHHU n *URWHGLVSOD\YRRUWHNHQV n (HQKRRIGVWXN,QppQRRJRSVODJLQGHKDQGOHLGLQJRPVQHOLQIRUPDWLH WHYLQGHQ n 7RHSDVVLQJHQYRRUKHWRSORVVHQYDQHFRQRPLVFKHHQILQDQFLsOH WDNHQ 7LPH9DOXHRI0RQH\/HQLQJHQVSDUHQOHDVHVHQ DPRUWLVDWLHVFKHPD·V 5HQWHFRQYHUVLH1RPLQDOHHQHIIHFWLHYHUHQWHYRHW &DVKIORZV1HWWRKXLGLJHZDDUGHHQLQWHUQUHQGHPHQW (FRQRPLVFKHSHUFHQWDJHV3URFHQWXHOHYHUDQGHULQ JHQEUXWRZLQVWHQPDUJHEHUHNHQLQJHQ 6WDWLVWLHNHQ*HPLGGHOGHVWDQGDDUGGHYLDWLHFRUUH ODWLHFRsIILFLsQWHQYHUZDFKWLQJHQPHWEHKXOSYDQOLQHDLUH UHJUHVVLHHQYHOHDQGHUHVWDWLVFKHEHUHNHQLQJHQ n *HQRHJJHKHXJHQRPHHQHHUVWHFDVKIORZHQFDVKIORZJURHSHQ PHWHONPD[LPDDOFDVKIORZVRSWHVODDQ n 7LHQJHQXPPHUGHRSVODJUHJLVWHUV n *HPDNNHOLMNWRHJDQNHOLMNHIXQFWLHVGRRUHHQJHULQJDDQWDO WRHWVDDQVODJHQZDDUGRRUKHWJHEUXLNZRUGWYHUHHQYRXGLJG 0RJHOLMNKHLGWRWDXWRPDWLVFKHYHUKRJLQJELMDPRUWLVDWLHV FKHPD·V /DEHOVYRRUDPRUWLVDWLHHQFDVKIORZV $XWRPDWLVFKHFRQVWDQWH 'ULHWRHWVHQJHKHXJHQ n ,QGHKDQGOHLGLQJ]LMQYHOHYRRUEHHOGHQRSJHQRPHQGLHXPHWHONDDU NXQWFRPELQHUHQYRRUXZVSHFLILHNHVLWXDWLH

4

Welkom bij de HP 10BII


Inhoud

1

11 11 12 13 14 15 16 17 18 19 21

In één oogopslag... %DVLVLGHHsQ³,QppQRRJRSVODJ 3URFHQWHQ³,QppQRRJRSVODJ *HKHXJHQWRHWVHQ³,QppQRRJRSVODJ« 7LPH9DOXHRI0RQH\790 ³,QppQRRJRSVODJ« 790:DWJHEHXUWHUDOV«³,QppQRRJRSVODJ« $PRUWLVDWLH³,QppQRRJRSVODJ« 5HQWHYRHWFRQYHUVLHV³,QppQRRJRSVODJ« ,55<5HQ139³,QppQRRJRSVODJ« 6WDWLVWLHN³,QppQRRJRSVODJ« 7RHWVHQ

23 23 23 23 25 25 25 25 26 27 28 28 28 29 30 30 31 31 31 32 32

Om te beginnen $DQHQXLW]HWWHQ 'HKHOGHUKHLGYDQGHGLVSOD\DDQSDVVHQ (HQYRXGLJHUHNHQNXQGLJHEHUHNHQLQJHQ 'HGLVSOD\HQKHWWRHWVHQERUGEHJULMSHQ &XUVRU +HWZLVVHQYDQGHFDOFXODWRU +HWJHKHXJHQZLVVHQ ,QGLFDWRUV 6KLIWWRHWV 6WDWLVWLHNWRHWV ,1387WRHWV 6:$3WRHWV :LVNXQGLJHIXQFWLHV +HWIRUPDDWYDQJHWDOOHQWRQHQ +HWDDQWDOJHWRRQGHGHFLPDOHQDDQJHYHQ :HWHQVFKDSSHOLMNHQRWDWLH *HWDOOHQPHWYROOHGLJHQDXZNHXULJKHLGWRQHQ 3XQWHQNRPPDYHUZLVVHOHQ +HWDIURQGHQYDQJHWDOOHQ 0HOGLQJHQ Inhoud

5


2

33 33 33 34 34 35 35 36 36

3

37

42 43 43

Het opslaan van getallen en rekenkundige bewerkingen +HWJHEUXLNYDQRSJHVODJHQJHWDOOHQELMEHUHNHQLQJHQ +HWJHEUXLNYDQFRQVWDQWHQ +HWJHEUXLNYDQKHW0UHJLVWHU +HWJHEUXLNYDQJHQXPPHUGHUHJLVWHUV 5HNHQNXQGLJHEHZHUNLQJHQXLWYRHUHQELQQHQHHQ UHJLVWHU 5HNHQNXQGLJHEHZHUNLQJHQXLWYRHUHQ 0DFKWYHUKHIILQJVRSHUDWRU +HWJHEUXLNYDQKDDNMHVLQEHUHNHQLQJHQ

45 45 46 47 47 47 48 49 49 49 51

Financiële problemen in beeld brengen +HWEHQDGHUHQYDQHHQILQDQFLHHOSUREOHHP +HWWHNHQYDQGHFDVKIORZ 3HULRGHVHQFDVKIORZV (QNHOYRXGLJHHQVDPHQJHVWHOGHUHQWH (QNHOYRXGLJHUHQWH 6DPHQJHVWHOGHUHQWH 'HUHQWHYRHW 7ZHHYHUVFKLOOHQGHILQDQFLsOHYUDDJVWXNNHQ +HWKHUNHQQHQYDQHHQ790YUDDJVWXN +HWKHUNHQQHQYDQHHQFDVKIORZYUDDJVWXN

37 37 39 40 41

4

6

Economische percentages 3URFHQWWRHWV (HQSHUFHQWDJHEHUHNHQHQ (HQSHUFHQWDJHRSWHOOHQRIDIWUHNNHQ 3URFHQWXHOHYHUDQGHULQJ %HUHNHQLQJYDQPDUJHHQEUXWRZLQVW 0DUJHEHUHNHQLQJHQ %HUHNHQLQJHQYDQGHEUXWRZLQVWWHQRS]LFKWHYDQGH NRVWHQ 0DUJHHQEUXWRZLQVWWHJHOLMNHUWLMGJHEUXLNHQ

Inhoud


5

53 53 55 55 55 61 64 68 73 74 75

“Time Value of Money”-berekeningen +HWJHEUXLNYDQGH790IXQFWLH 790UHJLVWHUVZLVVHQ %HJLQHQ(LQGPRGXV +HWEHUHNHQHQYDQOHQLQJHQ %HUHNHQLQJHQPHWVSDDUV\VWHPHQ /HDVHEHUHNHQLQJHQ $PRUWLVDWLH 5HQWHYRHWFRQYHUVLHV ,QYHVWHULQJHQPHWYHUVFKLOOHQGHSHULRGHVYDQVDPHQ VWHOOLQJ 6DPHQVWHOOLQJVHQEHWDOLQJVSHULRGHVYHUVFKLOOHQ

6

77 77 79 79 80 81 82 85 86

Cashflowberekeningen +HWJHEUXLNHQYDQGHFDVKIORZIXQFWLH 139HQ,55<5+HWYHUGLVFRQWHUHQYDQFDVKIORZV &DVKIORZVJURHSHUHQ &DVKIORZVLQYRHUHQ &DVKIORZVEHNLMNHQHQYHUYDQJHQ 'HQHWWRKXLGLJHZDDUGHEHUHNHQHQ +HWLQWHUQHUHQGHPHQWEHUHNHQHQ $XWRPDWLVFKHRSVODJYDQ,55<5HQ139

7

87 87 88 88 88 89 89 89 90 91 93 96

Statistische berekeningen 6WDWLVWLVFKHJHJHYHQVZLVVHQ 6WDWLVWLVFKHJHJHYHQVLQYRHUHQ 6WDWLVWLHNHQPHWppQYDULDEHOH 6WDWLVWLHNHQPHWWZHHYDULDEHOHQHQJHZRJHQJHPLGGHOGH 6WDWLVWLVFKHJHJHYHQVYHUEHWHUHQ 9HUEHWHUHQYDQJHJHYHQVEHVWDDQGHXLWppQYDULDEHOH 9HUEHWHUHQYDQJHJHYHQVEHVWDDQGHXLWWZHHYDULDEHOHQ 6DPHQYDWWLQJYDQVWDWLVWLVFKHEHUHNHQLQJHQ *HPLGGHOGHVWDQGDDUGGHYLDWLHHQVRPPDWLHVWDWLVWLHNHQ /LQHDLUHUHJUHVVLHHQEHQDGHULQJ *HZRJHQJHPLGGHOGH

Inhoud

7


8

99 99 99 100 101 102 102 102 104

117 118 118 120

Extra voorbeelden (FRQRPLVFKHWRHSDVVLQJHQ +HWYDVWVWHOOHQYDQHHQYHUNRRSSULMV 9HUZDFKWLQJHQJHEDVHHUGRSKLVWRULVFKHJHJHYHQV .RVWHQLQGLHQQLHWFRQWDQWZRUGWEHWDDOG /HQLQJHQHQK\SRWKHNHQ (QNHOYRXGLJHMDDUOLMNVHUHQWH &RQWLQXHVDPHQVWHOOLQJYDQUHQWH 2SEUHQJVWYDQHHQYHUGLVFRQWHHUGHRISUHPLH K\ SRWKHHN -DDUOLMNVSHUFHQWDJHYRRUHHQOHQLQJPHWNRVWHQ /HQLQJPHWHHQDIZLMNHQGHHHUVWHSHULRGH (HQDXWROHQLQJ ´&DQDGHVHK\SRWKHHNµ 790EHUHNHQLQJHQYRRU´ZDWDOVµVFHQDULR·V 6SDUHQ 6SDUHQYRRUKRJHUHVWXGLHV .DSLWDDOWRHQDPHGLHRQEHODVWLVWRGDWGH]HZRUGWRSJ HQRPHQ :DDUGHYDQHHQEHODVWEDUHSHQVLRHQUHNHQLQJ 9RRUEHHOGHQPHWFDVKIORZ :UDSDURXQGK\SRWKHNHQ 1HWWRWRHNRPVWLJHZDDUGH

123 123 125 125 125 125 126 127 128 128 129 129 130

Hulp, Batterijen en Service $QWZRRUGHQRSGHPHHVWYRRUNRPHQGHYUDJHQ 2PJHYLQJVIDFWRUHQ 9RHGLQJHQ%DWWHULMHQ %DWWHULMLQGLFDWRU %DWWHULMVSHFLILFDWLHV %DWWHULMHQSODDWVHQ 9DVWVWHOOHQRIGHFDOFXODWRUVHUYLFHQRGLJKHHIW %HSHUNWJDUDQWLHEHZLMVYRRUppQMDDU :DWRQGHUGHJDUDQWLHYDOW :DWQLHWRQGHUGHJDUDQWLHYDOW .ODQWHQWUDQVDFWLHVLQKHW9HUHQLJG.RQLQNULMN $OVGHFDOFXODWRUVHUYLFHQRGLJKHHIW

105 108 109 110 111 113 113 115

A

8

Inhoud


B

C

130 130 131 131 131 132 133

6HUYLFHDGUHVVHQ 6HUYLFHNRVWHQ 9HU]HQGLQVWUXFWLHV *DUDQWLHRSVHUYLFH 6HUYLFHFRQWUDFWHQ 9HUGHUHLQIRUPDWLH 7HUPHQHQFRQGLWLHVYRRUGHHLQGJHEUXLNHU

135 135 135 136 136 137 137 138 138 138 139 139 140 141

Nog meer berekeningen ,55<5%HUHNHQLQJHQ 0RJHOLMNHUHVXOWDWHQELMKHWEHUHNHQHQYDQ,55<5 ,55<5VWRSSHQHQRSQLHXZEHJLQQHQ (HQVFKDWWLQJLQYRHUHQYRRU,55<5 *HYROJHQYDQKHWJHEUXLNYDQΣ²YRRUKHWYHUEHWHUHQ YDQJHJHYHQV *HWDOOHQEHUHLN )RUPXOHV %HUHNHQLQJYDQPDUJHHQEUXWRZLQVW 7LPH9DOXHRI0RQH\790 $PRUWLVDWLH 5HQWHYRHWFRQYHUVLHV &DVKIORZEHUHNHQLQJHQ 6WDWLVWLHN

143

Meldingen

145

Index

Inhoud

9



In één oogopslag... *HEUXLNGLWKRRIGVWXNDOVXUHHGVEHNHQGEHQWPHWKHWJHEUXLNYDQHHQ FDOFXODWRURIPHWILQDQFLsOHFRQFHSWHQ8NXQWKHWRRNDOVQDVODJZHUN JHEUXLNHQ'HUHVWYDQGHKDQGOHLGLQJEHVWDDWXLWXLWOHJHQYRRUEHHOGHQ YDQGHLGHHsQGLHLQGLWKRRIGVWXNQDDUYRUHQZRUGHQJHEUDFKW

Basisideeën—In één oogopslag...

1* * R %*j *& *W Toetsen:

[oranje label]

Display:

Beschrijving:

0,00

=HWGHFDOFXODWRUDDQ 7RRQWGHVKLIWLQGLFDWRU SHIFT *DDWZHHUXLWGHVKLIW LQVWHOOLQJ :LVWKHWODDWVWHWHNHQ :LVWGHGLVSOD\ :LVWKHWVWDWLVWLVFKH JHKHXJHQ :LVWKHWKHOHJHKHX JHQ =HWGHFDOFXODWRUXLW

0,00 0,00 12_ 0,00 0,00 0,00

In één oogopslag...

11


Procenten—In één oogopslag...

D7 c]

3URFHQW .RVWHQ 3ULMV 0DUJH %UXWRZLQVW

7HOELMRS

D Toetsen:

Display:

Beschrijving:

17,50

9RHUWJHWDOLQ 7HOWRS

20,13

%HUHNHQGHPDUJHDOVGHNRVWHQJHOLMN]LMQDDQHQGHYHUNRRSSULMV LV

7 c ]

15,00 22,00 31,82

9RHUWGHNRVWHQLQ 9RHUWGHSULMVLQ %HUHNHQWGHPDUJH

$OVGHNRVWHQ]LMQHQGHEUXWRZLQVWLVZDWLVGDQGH YHUNRRSSULMV"

7 c

12


20,00 33,00 26,60

9RHUWGHNRVWHQLQ 9RHUWGHEUXWRZLQVWLQ %HUHNHQWGHSULMV


Geheugentoetsen—In één oogopslag…

- a *!

6ODDWHHQEHZHUNLQJPHWHHQFRQVWDQWHRS 6ODDWHHQZDDUGHRSLQKHW0UHJLVWHUJHKHXJHQSODDWV 9UDDJWHHQZDDUGHRSXLWKHW0UHJLVWHU 7HOWHHQZDDUGHRSELMKHWJHWDOGDWLQKHW0UHJLVWHULV RSJHVODJHQ 6ODDWHHQZDDUGHRSLQHHQJHQXPPHUGUHJLVWHU 9UDDJWHHQZDDUGHRSXLWHHQJHQXPPHUGUHJLVWHU

9HUPHQLJYXOGLJHQPHWZDDUELM´ïµDOVHHQEHZHUNLQJPHW HHQFRQVWDQWHZRUGWRSJHVODJHQ

" *! % Toetsen:

Display:

Beschrijving:

7,00

6ODDW´ïµDOVHHQ EHZHUNLQJPHWHHQFRQVWDQWH RS 9HUPHQLJYXOGLJWï 9HUPHQLJYXOGLJWï 9HUPHQLJYXOGLJWï

119,00 154,00 175,00

6ODLQUHJLVWHURSHQYUDDJKHWYHUYROJHQVRS 519,00 0,00 519,00

6ODDWLQUHJLVWHURS :LVWGHGLVSOD\ 9UDDJWUHJLVWHURS


13


Time Value of Money (TVM)—In één oogopslag… 9RHUYLHUZLOOHNHXULJHZDDUGHQLQHQEHUHNHQGHYLMIGH ZDDUGH

P. 2 /*O *b

(HQPLQWHNHQLQGHGLVSOD\EHWHNHQWHHQEHWDDOGEHGUDJKHW RQWYDQJHQEHGUDJLVSRVLWLHI $DQWDOEHWDOLQJHQ 5HQWHSHUMDDU +XLGLJHZDDUGH %HWDOLQJ 7RHNRPVWLJHZDDUGH %HJLQRI(LQGPRGXV ´$DQWDOEHWDOLQJHQSHUMDDUµPRGXV

$OVX39 JHGXUHQGHPDDQGHQOHHQW1 WHJHQHHQUHQWH YDQ,<5 KRHJURRW]LMQGDQGHPDDQGHOLMNVHEHWDOLQJHQ" 6WHOGH(LQGPRGXVLQ'UXNRS

*b P . / 2 Toetsen:

14


*O

DOVXGHBEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 9RHUWKHWDDQWDOEHWDOLQJHQLQ 9RHUWGHUHQWHSHUMDDULQ 9RHUWGHKXLGLJHZDDUGHLQ 9RHUWGHWRHNRPVWLJHZDDUGH LQ %HUHNHQWGHEHWDOLQJDOVGH]H DDQKHWHLQGHYDQGHSHULRGH ZRUGWEHWDDOG

360,00 10,00 14.000,00 0,00 –122,86


TVM Wat gebeurt er als…—In één oogopslag… +HWLVQLHWQRGLJGDWYRRULHGHUYRRUEHHOGGH790ZDDUGHQ RSQLHXZZRUGHQLQJHYRHUG+RHYHHONXQWXOHQHQPHWGH ZDDUGHQGLHX]RMXLVWKHEWLQJHYRHUGSDJLQD DOVX EHWDOLQJHQYDQZLOWGRHQ"

(2 Toetsen:

.

Display:

Beschrijving:

–100,00

9RHUWKHWQLHXZH EHGUDJYDQGHEHWDOLQJ LQ+HWXLWEHWDDOGH EHGUDJLVQHJDWLHI %HUHNHQWKHWEHGUDJ GDWXNXQWOHQHQ

11.395,08

+RHYHHONXQWXOHQHQWHJHQHHQUHQWHYDQ"

. 2

9,50 11.892,67

10,00

14.000,00

–122,86

9RHUWGHQLHXZHUHQW HYRHWLQ %HUHNHQWGHQLHXZH KXLGLJHZDDUGHYRRU HHQEHWDOLQJYDQ ELMHHQUHQWH YDQ 9RHUWGH RRUVSURQNHOLMNHUHQWH RSQLHXZLQ 9RHUWGHRRU VSURQNHOLMNHKXLGLJH ZDDUGHRSQLHXZLQ %HUHNHQWGH RRUVSURQNHOLMNH EHWDOLQJ


15


Amortisatie—In één oogopslag… 1DKHWEHUHNHQHQYDQHHQEHWDOLQJPHW7LPH9DOXHRI 0RQH\790 YRHUWXGHSHULRGHVLQZDDULQ JHDPRUWLVHHUGZRUGWHQGUXNWXYHUYROJHQVRS 'UXNGDQRS RPGHUHQWHKRRIGVRPHQVDOGRZDDUGHQ WHEHNLMNHQUHVSHFWLHYHOLMNDDQJHGXLGGRRUGHPRIN INT HQBAL LQGLFDWRU

*

$PRUWLVHHUPHWEHKXOSYDQKHWYRULJH790YRRUEHHOGSDJLQD HHQ HQNHOYRXGLJHEHWDOLQJHQYHUYROJHQVHHQUHHNVEHWDOLQJHQ $PRUWLVHHUGHVWHEHWDOLQJYDQGHOHQLQJ

0 * 0 * Toetsen:

Display:

Beschrijving:

20,00

9RHUWGHEHWDOLQJLQGLHPRHW JHDPRUWLVHHUGZRUGHQ *HHIWGHEHWDOLQJZHHUGLH PRHWJHDPRUWLVHHUGZRUGHQ *HHIWGHKRRIGVRPZHHU *HHIWGHUHQWHZHHU%HWDDOGH EHGUDJHQ]LMQQHJDWLHI *HHIWKHWVDOGRZHHU

20 – 20 –7,25 –115,61 13.865,83

$PRUWLVHHUGHVWHWRWHQPHWGHGHEHWDOLQJHQYDQGHOHQLQJ

16


12_

1 – 12 –77,82 –1.396,50 13.922,18

9RHUWGHUHHNVEHWDOLQJHQLQ GLHPRHWHQJHDPRUWLVHHUG ZRUGHQ *HHIWGHUHHNVYDQSHULRGHV EHWDOLQJHQ ZHHU *HHIWGHKRRIGVRPZHHU *HHIWGHUHQWHZHHU%HWDDOGH EHGUDJHQ]LMQQHJDWLHI *HHIWKHWVDOGRZHHU


Rentevoetconversies—In één oogopslag… 2PWHFRQYHUWHUHQWXVVHQGHQRPLQDOHHQHIIHFWLHYHUHQWH YRHUWXGHEHNHQGHUHQWHHQKHWDDQWDOSHULRGHVSHUMDDULQ HQEHUHNHQWXYHUYROJHQVGHRQEHNHQGHUHQWH

* *Z *b

1RPLQDDOUHQWHSHUFHQWDJH (IIHFWLHIUHQWHSHUFHQWDJH 3HULRGHVSHUMDDU

%HUHNHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYDQHHQQRPLQDOHUHQWHYDQGLH PDDQGHOLMNVVDPHQJHVWHOGZRUGW

* *b *Z Toetsen:

Display:

Beschrijving:

10,00

9RHUWGHQRPLQDOH UHQWHLQ 9RHUWKHWDDQWDO EHWDOLQJHQSHUMDDULQ %HUHNHQWGHMDDUOLMNVH HIIHFWLHYHUHQWH

12,00 10,47


17


IRR/YR en NPV—In één oogopslag…

*b , *C *9 *N

$DQWDOSHULRGHVSHUMDDUVWDQGDDUGZDDUGHLV &DVKIORZVPD[LPDDO´MµJHHIWKHWQXPPHUYDQGHFDVK IORZJURHSDDQ $DQWDONHUHQGDWFDVKIORZ´MµDFKWHUHHQYROJHQVYRRUNRPW ,QWHUQUHQGHPHQWSHUMDDU 1HWWRFRQWDQWHZDDUGH

:DWLVGH,55<5DOVXHHQLQLWLsOHXLWJDDQGHFDVKIORZKHEWYDQ JHYROJGGRRUPDDQGHOLMNVLQNRPHQGHFDVKIORZVYDQ HQ":DWLVGH,55SHUPDDQG"

*& *b (, , , *C Toetsen:

, *9 d . *N

Display:

Beschrijving:

0,00 12,00

:LVWKHWKHOHJHKHXJHQ 6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 9RHUWGHLQLWLsOHXLWJDDQGH FDVKIORZLQ 9RHUWGHHHUVWHFDVKIORZLQ 9RHUWGHWZHHGHFDVKIORZLQ 9RHUWLQKRHYDDNGHFDVK IORZDFKWHUHHQYROJHQV YRRUNRPW 9RHUWGHGHUGHFDVKIORZLQ %HUHNHQW,55<5 %HUHNHQW,55SHUPDDQG

–40.000,00 4.700,00 7.000,00 2,00

23.000,00 15,96 1,33

:DWLVGH139DOVGHGLVFRQWRUHQWHLV" 10

18


10,00 622,85

9RHUW,<5LQ %HUHNHQW139


Statistiek—In één oogopslag…

*j A*@ 0 A 0 *@ *$*i *E *:*i *M*i *3*i *4 *4*i JHWDO JHWDO

JHWDO

JHWDO

JHWDO

JHWDO

\ZDDUGH [ZDDUGH

:LVWVWDWLVWLVFKHUHJLVWHUV 9RHUWVWDWLVWLVFKHJHJHYHQVPHWppQYDULDEHOHLQ 9HUZLMGHUWVWDWLVWLVFKHJHJHYHQVPHWppQYDULD EHOH 9RHUWVWDWLVWLVFKHJHJHYHQVPHWWZHHYDULDEHOHQ LQ 9HUZLMGHUWVWDWLVWLVFKHJHJHYHQVPHWWZHHYDULD EHOHQ *HPLGGHOGHQYDQ[HQ\ *HPLGGHOGHYDQ[JHZRJHQGRRU\ 6WHHNSURHIVWDQGDDUGGHYLDWLHYRRU[HQ\ 3RSXODWLHVWDQGDDUGGHYLDWLHYRRU[HQ\ %HQDGHULQJYDQ[HQGHFRUUHODWLHFRsIILFLsQW %HQDGHULQJYDQ\ 6QLMSXQWPHWGH\DVHQGHKHOOLQJ

%HUHNHQPHWEHKXOSYDQGHYROJHQGHJHJHYHQVKHWJHPLGGHOGHYDQ[HQ\ GHVWHHNSURHIVWDQGDDUGGHYLDWLHYRRU[HQ\HQKHWVQLMSXQWPHWGH\DV HQGHULFKWLQJVFRsIILFLsQWYDQGHOLMQGLHGHOLQHDLUHUHJUHVVLHZHHUJHHIW %HUHNHQYHUYROJHQVPHWVRPPDWLHVWDWLVWLHNHQQHQΣ[\ x-gegevens

2

4

6

y-gegevens

50

90

160


19


*j 0A 0A 0A *$ *i *: *i *4 Toetsen:

*i ) )

20


Display:

Beschrijving:

0,00

:LVWGHVWDWLVWLVFKHUHJLVWHUV

1,00

9RHUWKHWHHUVWH[\SDDULQ

2,00

9RHUWKHWWZHHGH[\SDDULQ

3,00

9RHUWKHWGHUGH[\SDDULQ

4,00

*HHIWKHWJHPLGGHOGHYDQGH[ ZDDUGHQZHHU

100,00

*HHIWKHWJHPLGGHOGHYDQGH\ ZDDUGHQZHHU

2,00

*HHIWGHVWHHNSURHIVWDQGDDUG GHYLDWLHYRRU[ZHHU

55,68

*HHIWGHVWHHNSURHIVWDQGDDUG GHYLDWLHYRRU\ZHHU

–10,00

*HHIWKHWVQLMSXQWYDQGH UHJUHVVLHOLMQPHWGH\DVZHHU EHQDGHUGH yˆ ZDDUGHYRRU [

27,50

*HHIWGHKHOOLQJYDQGHUHJUHVV LHOLMQZHHU

3,00

*HHIWQKHWDDQWDOLQJHYRHUGH JHJHYHQVZHHU

1.420,00

*HHIWΣ[\VRPYDQGH SURGXFWHQYDQ[HQ\ZDDUGHQ


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. n tot en met Σxy: 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)


21



1 Om te beginnen Aan- en uitzetten

1

8]HWXZ+3%,,DDQGRRURS WHGUXNNHQ8]HWGH FDOFXODWRUXLWGRRURSGHRUDQMHVKLIWWRHWV WHGUXNNHQ HQYHUYROJHQVRS WHGUXNNHQZRUGWRRNDOVYROJW DDQJHJHYHQ

1 *W

*

$DQJH]LHQGHFDOFXODWRUHHQSHUPDQHQWJHKHXJHQKHHIW ZRUGWGHRSJHVODJHQLQIRUPDWLHQLHWDDQJHWDVWDOVGH FDOFXODWRUXLWJH]HWZRUGW2PVWURRPWHEHVSDUHQVFKDNHOWGHFDOFXODWRU ]LFK]HOIRQJHYHHUPLQXWHQQDGDWKLMYRRUKHWODDWVWJHEUXLNWZHUGXLW 'HFDOFXODWRUJHEUXLNWWZHHOLWKLXPEDWWHULMHQ$OVXKHWV\PERROYRRU ODJHEDWWHULMVSDQQLQJ LQGHGLVSOD\]LHWPRHWHQGHEDWWHULMHQ ZRUGHQYHUYDQJHQ5DDGSOHHJDDQKDQJVHO$YRRUPHHULQIRUPDWLH

De helderheid van de display aanpassen

1LQJHGUXNWHQ

2PGHKHOGHUKHLGYDQGHGLVSOD\WHYHUDQGHUHQKRXGWX GUXNWXWHJHOLMNHUWLMGRS RI

Eenvoudige rekenkundige berekeningen Rekenkundige operatoren. ,QGHYROJHQGHYRRUEHHOGHQ]LHWXKHW JHEUXLNYDQGHUHNHQNXQGLJHRSHUDWRUHQ HQ

" d

$OVXDFKWHUHHQYROJHQVRSPHHUGDQppQRSHUDWRUGUXNWELMYRRUEHHOGRS

" ZRUGWHQNHOPHWGHODDWVWJHGUXNWHWRHWVUHNHQLQJ JHKRXGHQ

1: Om te beginnen

23


$OVXELMKHWLQYRHUHQYDQHHQJHWDOHHQW\SHIRXWPDDNWGUXNGDQRS RP]RGHIRXWLHYHFLMIHUVWHZLVVHQ Toetsen:

R

Display:

Beschrijving:

87,18

7HOWHQRS

$OVHHQEHUHNHQLQJDIJHVORWHQLVGRRU LQWHGUXNNHQ EHJLQWGRRUKHW LQGUXNNHQYDQHHQFLMIHUWRHWVHHQQLHXZHEHUHNHQLQJ

"

240,92

%HUHNHQWï

$OVXQDGDWXGHEHUHNHQLQJKHEWXLWJHYRHUGRSHHQRSHUDWRUWRHWVGUXNW NXQWXYHUGHUJDDQPHWGHEHUHNHQLQJ

356,42

6OXLWGHEHUHNHQLQJYDQ DI

8NXQWNHWWLQJEHZHUNLQJHQXLWYRHUHQGRRUQLHWQDLHGHUHVWDSRS WH GUXNNHQ

"d

36,92

40,57

d

'RRURS WHGUXNNHQ NRPWGHWXVVHQRSORVV LQJ ï LQGH GLVSOD\ 'HEHZHUNLQJLVNODDU

.HWWLQJEHZHUNLQJHQZRUGHQJHwQWHUSUHWHHUGLQGHYROJRUGHZDDURS]LM ZRUGHQLQJHYRHUG%HUHNHQ[

"

13,00 39,00

7HOWRS 9HUPHQGLJYXOGLJWï

(DOVXKHWWHNHQZLOW

Negatieve getallen. 9RHUKHWJHWDOLQHQGUXNRS

YHUDQGHUHQ%HUHNHQ²¸ Toetsen:

( d 24

1: Om te beginnen

Display:

Beschrijving:

–75_

9HUDQGHUWKHWWHNHQ YDQ %HUHNHQWKHWUHVXOWDDW

–25,00


De display en het toetsenbord begrijpen Cursor 8]LHWGHFXUVRUB DOVXHHQJHWDOLQYRHUW

Het wissen van de calculator

R

$OVGHFXUVRULQGHGLVSOD\VWDDWZRUGWGRRU KHWODDWVW LQJHYRHUGHFLMIHUJHZLVW,QDOOHDQGHUHJHYDOOHQZRUGWGRRU GHGLVSOD\JHZLVWHQGHEHZHUNLQJJHDQQXOHHUG

R

%

$OVXRS GUXNWELMKHWLQYRHUHQYDQHHQJHWDONRPWLQ GHGLVSOD\WHVWDDQ$QGHUVZLVW GHJHJHYHQVGLHLQGH GLVSOD\VWDDQHQZRUGWGHKXLGLJHEHZHUNLQJJHDQQXOHHUG

%

Meldingen verwijderen.$OVGH+3%,,HHQIRXWPHOGLQJWRRQW YHUZLMGHUWXGHPHOGLQJPHW RIPHW HQNULMJWXGHRRUVSURQNHOLMNH LQKRXGZHHULQGHGLVSOD\WH]LHQ=LH´0HOGLQJHQµRSSDJLQD YRRU HHQYROOHGLJHOLMVWYDQPHOGLQJHQHQKXQEHWHNHQLV

R

%

Het geheugen wissen

Toetsen

*& *j

Beschrijving

:LVWKHWKHOHJHKHXJHQ6WHOWGHLQVWHOOLQJHQ QLHW RSQLHXZLQ :LVWKHWVWDWLVFKHJHKHXJHQ

,QVWHOOLQJHQRSGH+3%,,]LMQKHWDDQWDOEHWDOLQJHQSHUMDDUSDJLQD %HJLQHQ(LQGSDJLQD HQGH GLVSOD\IRUPDWHQSDJLQD

1: Om te beginnen

25


2PKHWJHKHOHJHKHXJHQWHZLVVHQHQRPGHFDOFXODWRURSQLHXZLQWH VWHOOHQGUXNWXRS KRXGWXGH]HLQJHGUXNWZDDUQDXWHJHOLMNHUWLMGRS HQ GUXNWHQGH]HHYHQHHQVLQJHGUXNWKRXGW$OVXGHGULHWRHWVHQ ORVODDWLVKHWJHKHOHJHKHXJHQJHZLVW2SGHGLVSOD\YHUVFKLMQWGH PHOGLQJAll Clear

P /

1

Indicators ,QGLFDWRUV]LMQV\PEROHQLQGHGLVSOD\GLHGHVWDWXVYDQGHFDOFXODWRU DDQJHYHQ Indicator SHIFT

STATS

PEND BEGIN INPUT

AMORT BAL INT PRIN PER C - FLOW

26

1: Om te beginnen

Status

*

'HVKLIWWRHWV ZHUGLQJHGUXNW$OVXHHQDQGHUH WRHWVLQGUXNWZRUGWGHIXQFWLHGLHERYHQGHWRHWV LQKHWRUDQMHLVDDQJHJHYHQXLWJHYRHUG 'HVWDWLVWLHNWRHWV LVDFWLHI$OVXHHQDQGHUH WRHWVLQGUXNWZRUGWGHIXQFWLHXLWJHYRHUGGLHERYHQ GHWRHWVLQKHWSDDUVLVDDQJHJHYHQ (UPRHWYRRUGHEHZHUNLQJQRJHHQRSHUDQG ZRUGHQLQJHYRHUG 'H%HJLQPRGXVLVDFWLHISDJLQD GHEHWDOLQJHQ JHEHXUHQDDQKHWEHJLQYDQHHQSHULRGH 'H WRHWVZHUGLQJHGUXNWHQHUZHUGHHQQXP PHURSJHVODJHQ 'HEDWWHULMHQ]LMQELMQDOHHJSDJLQD 'HDPRUWLVDWLHLQGLFDWRULV]LFKWEDDUVDPHQPHW ppQYDQGHYROJHQGHYLHULQGLFDWRUV +HWVDOGRYDQHHQDPRUWLVDWLHZRUGWZHHUJH JHYHQSDJLQD 'HUHQWHYDQHHQDPRUWLVDWLHZRUGWZHHUJH JHYHQSDJLQD 'HKRRIGVRPYDQHHQDPRUWLVDWLHZRUGWZHHUJH JHYHQSDJLQD (UZRUGWHHQDDQWDOSHULRGHVJHEUXLNWYRRUHHQ DPRUWLVDWLHSDJLQD 'HFDVKIORZLQGLFDWRULV]LFKWEDDUVDPHQPHWppQ YDQGHYROJHQGHWZHHLQGLFDWRUV

)

0


Indicator CF N

ERROR TVM FULL STAT

FUNC STAT

Status

+HWQXPPHUYDQGHFDVKIORZLVNRUW]LFKWEDDU ZDDUQDGHFDVKIORZZRUGWZHHUJHJHYHQ +HWQXPPHUYDQGHFDVKIORZLVNRUW]LFKWEDDU ZDDUQDKHWDDQWDONHUHQGDWHHQFDVKIORZDFKW HUHHQYROJHQVYRRUNRPWZRUGWZHHUJHJHYHQ 'HIRXWLQGLFDWRULV]LFKWEDDUVDPHQPHWppQYDQ GHYROJHQGHYLHULQGLFDWRUV (ULVHHQ790IRXWELMYRRUEHHOGRSORVVHQQDDU 3<5 (UZHUGHQPHHUGDQFDVKIORZVLQJHYRHUGRIHU ZHUGHQPHHUGDQQLHWRSJHORVWHKDDNMHVJHEUXLNW )RXWLHYHGDWDJHEUXLNWLQHHQVWDWLVWLVFKHEHUHNHQ LQJRILQGLHQQLHWZHHUJHJHYHQZRUGWHUZHUGHHQ VWDWLVWLVFKHEHUHNHQLQJXLWJHYRHUG (ULVHHQZLVNXQGLJHIRXWJHEHXUGELMYRRUEHHOG GHOHQGRRUQXO (UZHUGHHQVWDWLVWLVFKHEHUHNHQLQJXLWJHYRHUG

Shifttoets 9RRUELMQDDOOHWRHWVHQYDQGH+3%,,EHVWDDWHHQ WZHHGH´VKLIWHGµIXQFWLHGLHLQKHWRUDQMHERYHQGH EHWUHIIHQGHWRHWVVWDDW0HWGHRUDQMHVKLIWWRHWV NULMJW XWRHJDQJWRWGH]HIXQFWLHV

*

*

WHGUXNNHQ

$OVXRS GUXNWNULMJWXGHVKLIWLQGLFDWRUSHIFT WH ]LHQZDDUPHHZRUGWDDQJHJHYHQGDWGHVKLIWHGIXQFWLHV DFWLHI]LMQ'HSHIFT LQGLFDWRU]HWXXLWGRRUZHHURS

*

*

h

*h

8GUXNWELMYRRUEHHOGRS HQYHUYROJHQVRS HYHQHHQVDOV DDQJHJHYHQ RPKHWJHWDOLQGHGLVSOD\PHW]LFK]HOIWHYHUPHQLJYXOGLJHQ

1: Om te beginnen

27


Statistiektoets

)

'HVWDWLVWLHNWRHWV SDDUVJHNOHXUG ZRUGWJHEUXLNWRP WRHJDQJWHNULMJHQWRWVRPPDWLHVWDWLVWLHNHQXLWGH VWDWLVWLVFKHJHKHXJHQUHJLVWHUV

)

$OVXRS GUXNWNULMJWXGHVWDWLVWLHNLQGLFDWRUSTATS WH ]LHQ'LWEHWHNHQWGDWXppQYDQGH]HV VRPPDWLHVWDWLVWLHNHQNXQWRSURHSHQPHWGHYROJHQGH WRHWVDDQVODJ]LHSDJLQD

)

;

%LMYRRUEHHOGGUXNRS HQYHUYROJHQVRS RPGHVRPYDQGH LQJHYRHUGH[ZDDUGHQRSWHURHSHQ

INPUT-toets

0

'H WRHWVZRUGWJHEUXLNWRPWZHHJHWDOOHQWHVFKHLGHQ DOVXZHUNWPHWHHQIXQFWLHPHWWZHHYDULDEHOHQRIPHW VWDWLVWLHNHQPHWWZHHYDULDEHOHQ'H WRHWVNDQRRN ZRUGHQJHEUXLNWRPHHQZLVNXQGLJHEHZHUNLQJDOWLMGHQGH YHUZHUNLQJWHHYDOXHUHQLQGLWJHYDONULMJWXKHW]HOIGH UHVXOWDDWDOVGRRUKHWLQGUXNNHQYDQ

0

SWAP-toets

*i

'RRURS WHGUXNNHQZRUGWKHWYROJHQGHYHUZLVVHOG n 'HODDWVWHWZHHJHWDOOHQGLH]LMQLQJHYRHUGRP ELMYRRUEHHOGELMGHOHQHQDIWUHNNHQGHYROJRUGHWH YHUDQGHUHQ n 'HRSORVVLQJHQYDQHHQIXQFWLHGLHWZHHZDDUGHQ EHUHNHQW n 'H[HQ\ZDDUGHQELMVWDWLVWLVFKHWRHSDVVLQJHQ

28

1: Om te beginnen


Wiskundige functies Functies met één onbekende. :LVNXQGLJHIXQFWLHV

ZDDUppQRQEHNHQGHLQYRRUNRPWJHEUXLNHQKHWJHWDOLQGH GLVSOD\DOVRQEHNHQGH

Toetsen:

*T *[

Display:

Beschrijving:

9,45

%HUHNHQWGHYLHU NDQWVZRUWHO ZRUGWHHUVW EHUHNHQG 7HOWHQELM HONDDURS

0,42 3,99

Functies met twee onbekenden. $OVHUYRRUHHQ

IXQFWLHWZHHJHWDOOHQQRGLJ]LMQZRUGHQGH]HDOVYROJW LQJHYRHUGJHWDO JHWDOHQYHUYROJHQVGHXLWWHYRHUHQ EHZHUNLQJ$OVXRS GUXNWZRUGWGHKXLGLJH XLWGUXNNLQJEHUHNHQGHQ]LHWXGHINPUT LQGLFDWRU'RRU GHYROJHQGHWRHWVDDQVODJHQZRUGWELMYRRUEHHOGGH SURFHQWXHOHYHUDQGHULQJWXVVHQHQEHUHNHQG

0

Toetsen:

0 *6

0

Display:

Beschrijving:

17,00

9RHUWJHWDOLQGH INPUT LQGLFDWRUYHU VFKLMQW 9RHUWJHWDOLQ %HUHNHQWGHSURFHQWXHOH YHUDQGHULQJ

29_ 70,59

1: Om te beginnen

29


Het formaat van getallen tonen $OVXGH+3%,,YRRUKHWHHUVWDDQ]HWZRUGHQJHWDOOHQ LQWZHHGHFLPDOHQQDXZNHXULJJHWRRQGPHWHHQGHFLPDOH SXQW+HWDDQWDOFLMIHUVGDWXLQGHGLVSOD\]LHWZRUGW EHSDDOGGRRUGHJHWDOQRWDWLH $OVKHWUHVXOWDDWYDQHHQEHUHNHQLQJHHQJHWDOLVPHWPHHU VLJQLILFDQWHFLMIHUVGDQLQGHKXLGLJHQRWDWLHNDQZRUGHQ JHWRRQGZRUGWKHWJHWDODIJHURQG]RGDWKHWLQGHKXLGLJHGLVSOD\ LQVWHOOLQJSDVW 2QJHDFKWGHKXLGLJHGLVSOD\QRWDWLHZRUGWLHGHUJHWDORSJHVODJHQDOVHHQ FLMIHULJJHWDOGDWYDQHHQWHNHQLVYRRU]LHQPHWHHQGULHFLMIHULJH H[SRQHQWRRNYDQHHQWHNHQYRRU]LHQ

Het aantal getoonde decimalen aangeven *DDOVYROJWWHZHUNRPKHWDDQWDOJHWRRQGHGHFLPDOHQDDQWHJHYHQ 'UXNRS 9RHUKHWDDQWDOGHFLPDOHQWP LQGDWXZLOW]LHQ

*

Toetsen:

% * " * *

Display:

Beschrijving:

0,00

:LVWGHGLVSOD\ 7RRQWGULHGHFLPDOHQ

0,000 5,727 5,727360000 5,73

7RRQWQHJHQGHFL PDOHQ 7HUXJQDDUGHQRWDWLH PHWWZHHGHFLPDOHQ +HWJHWDOLQGHGLVSOD\ ZRUGWDIJHURQG

$OVHHQJHWDOWHJURRWRIWHNOHLQLVRPLQKHW',63IRUPDDWJHWRRQGWH ZRUGHQZRUGWKHWDXWRPDWLVFKLQGHZHWHQVFKDSSHOLMNHQRWDWLHJHWRRQG

30

1: Om te beginnen


Wetenschappelijke notatie 'HZHWHQVFKDSSHOLMNHQRWDWLHZRUGWJHEUXLNWYRRUJHWDOOHQ GLHWHJURRWRIWHNOHLQ]LMQYRRUGHGLVSOD\$OVX ELMYRRUEHHOGKHWJHWDO LQYRHUWLVKHWUHVXOWDDW(GDWEHWHNHQWppQNHHU WLHQWRWGHYHHUWLHQGHPDFKWRIZDDUELMGHGHFLPDOH NRPPDYHHUWLHQSODDWVHQQDDUUHFKWVZRUGWJHVFKRYHQ8 NXQWGLWJHWDOLQYRHUHQGRRU LQWHWRHWVHQ'H( EHWHNHQWGH´H[SRQHQWYDQWLHQµ

"

*'

9RRU]HHUNOHLQHJHWDOOHQNXQQHQH[SRQHQWHQRRNQHJDWLHIZRUGHQ+HW JHWDO]LHWXDOV(²GLWEHWHNHQWYLHUNHHUWLHQWRW GHQHJDWLHYHWZDDOIGHPDFKWRI´ZDDUELMGHGHFLPDOHNRPPD SODDWVHQQDDUOLQNVLVYHUVFKRYHQµ8NXQWGLWJHWDOLQYRHUHQGRRU LQWHWRHWVHQ

*'(

Getallen met volledige nauwkeurigheid tonen

*

'RRURS WHGUXNNHQVWHOWXGHFDOFXODWRULQRP JHWDOOHQ]RQDXZNHXULJPRJHOLMNWHWRQHQQXOOHQDFKWHU KHWJHWDOZRUGHQQLHWJHWRRQG $OVXWLMGHOLMNDOOHFLMIHUV YDQKHWJHWDOLQGHGLVSOD\ZLOWEHNLMNHQRQDIKDQNHOLMNYDQ GHLQJHVWHOGHJHWDOQRWDWLH GUXNWXRS HQKRXGWX LQJHGUXNW8]LHWKHWJHWDO]RODQJX LQJHGUXNWKRXGW 'HGHFLPDOHNRPPDZRUGWQLHWJHWRRQG

*

%HJLQPHWWZHHGHFLPDOHQ Toetsen:

d *

*

Display:

Beschrijving:

1,43

9RHUWGHGHOLQJXLW 7RRQWDOOHFLMIHUV

142857142857

Punt en komma verwisselen 8NXQWGHSXQWHQGHNRPPDPHWHONDDUYHUZLVVHOHQDOV GHFLPDDOVFKHLGLQJVWHNHQRIDOVVFKHLGLQJVWHNHQWXVVHQ FLMIHUV$QJHOVDNVLVFKHYHUVXVLQWHUQDWLRQDOHQRWDWLH GRRU RS WHGUXNNHQ

*

(pQPLOMRHQNDQELMYRRUEHHOGDOVZRUGHQ JHWRRQGRIDOV 1: Om te beginnen

31


Het afronden van getallen 'HFDOFXODWRUVODDWJHWDOOHQRSLQFLMIHUVHQUHNHQW HYHQHHQVPHWJHWDOOHQYDQFLMIHUV$OVGH QDXZNHXULJKHLGYDQFLMIHUVQLHWZHQVHOLMNLVNXQWXPHW KHWJHWDODIURQGHQQDDUGHQRWDWLHYDQGHGLVSOD\ YRRUGDWXKHWYRRUHHQYHUGHUHEHUHNHQLQJJHEUXLNW+HW DIURQGHQYDQFLMIHUVLV]HHUKDQGLJDOVXGHZHUNHOLMNH PDDQGHOLMNHEHWDOLQJHQGROODUVHQFHQWV ZLOWEHUHNHQHQ

*L Toetsen:

* *

Display:

Beschrijving:

9,87654321_

9RHUWHHQJHWDOLQPHW PHHUGDQWZHHGHFL PDOHQYHUVFKLOOHQGYDQ QXO 7RRQWWZHHGHFLPDOHQ 7RRQWDOOHFLMIHUV ]RQGHUGHGHFLPDOH SXQW]RODQJX LQJH GUXNWKRXGW 5RQGWDIRSWZHHGHFL PDOHQLQJHVWHOGGRRU KHWLQWRHWVHQYDQ KLHUYRRU 7RRQWKHWDIJHURQGHHQ RSJHVODJHQJHWDO

9,88 987654321000

*L

9,88

*

988000000000

*

Meldingen 'H+3%,,JHHIWPHOGLQJHQZHHURYHUGHVWDWXVYDQGHFDOFXODWRUZHHU RIODDWXZHWHQZDQQHHUXHHQYHUNHHUGHEHZHUNLQJSUREHHUWXLWWH YRHUHQ'RRURS RI WHGUXNNHQYHUZLMGHUWXGHPHOGLQJYDQGH GLVSOD\=LH´0HOGLQJHQµRSSDJLQD YRRUHHQYHUNODULQJYDQGH PHOGLQJHQ

% R

32

1: Om te beginnen


2 Economische percentages 8NXQWGH+3%,,JHEUXLNHQRPSHUFHQWDJHVSURFHQWXHOH YHUDQGHULQJHQNRVWHQSULMVPDUJHHQEUXWRZLQVWWHEHUHNHQHQ

Procenttoets

'H WRHWVKHHIWWZHHIXQFWLHVKHWEHUHNHQHQYDQHHQ SHUFHQWDJHHQKHWRSWHOOHQRIDIWUHNNHQYDQHHQ SHUFHQWDJH

Een percentage berekenen

D

'H WRHWVGHHOWHHQJHWDOGRRUWHQ]LMHUHHQSOXVRIHHQPLQWHNHQ DDQYRRUDIJDDW Voorbeeld. %HUHNHQYDQ Toetsen:

"

Display:

Beschrijving:

200,00

9RHUWLQ =HWRPLQHHQGHFL PDDOJHWDO 9HUPHQLJYXOGLJWPHW

0,25 50,00

2: Economische percentages

33


Een percentage optellen of aftrekken 8NXQWLQppQEHUHNHQLQJHHQSHUFHQWDJHRSWHOOHQRIDIWUHNNHQ Voorbeeld. 9HUPLQGHUPHW Toetsen:

Display:

Beschrijving:

200,00

9RHUWLQ 9HUPHQLJYXOGLJW PHW 7UHNWYDQDI

50,00 150,00

Voorbeeld. 8OHHQWYDQHHQYULHQGHQXNRPWRYHUHHQRPGH OHQLQJQDppQMDDUPHWHQNHOYRXGLJHUHQWHWHUXJWHEHWDOHQ:DWEHQWX GDQVFKXOGLJ" Toetsen:

Display:

Beschrijving:

87,50

%HUHNHQWGHUHQWHYDQ GHOHQLQJ 7HOWHQ ELMHONDDURSHQWRRQW EHGUDJGDWXPRHWWHU XJEHWDOHQ

1.337,50

Procentuele verandering %HUHNHQWGHSURFHQWXHOHYHUDQGHULQJWXVVHQWZHHJHWDOOHQ Q HQQ XLWJHGUXNWDOVSHUFHQWDJHYDQQ GRRUQ Q LQWHYRHUHQHQYHUYROJHQVRS WHGUXNNHQ

*6

0

Voorbeeld. %HUHNHQGHSURFHQWXHOHYHUDQGHULQJWXVVHQ HQ Toetsen:

0 *6

34

Display:

Beschrijving:

291,70

9RHUWQ LQ

8,60

%HUHNHQWGHSURFHQWX HOHYHUDQGHULQJ



Voorbeeld. %HUHNHQGHSURFHQWXHOHYHUDQGHULQJWXVVHQï HQ

Toetsen:

"0 *6

Display:

Beschrijving:

60,00

%HUHNHQWHQYRHUWQ LQ

38,33

%HUHNHQWSURFHQWXHOH YHUDQGHULQJ

Berekening van marge en brutowinst 'H+3%,,NDQNRVWHQYHUNRRSSULMVPDUJHRIEUXWRZLQVWEHUHNHQHQ Toepassing

Toetsen

0DUJH

7 , c, ]

%UXWRZLQVW

7 , c,

Beschrijving

'HPDUJHLVGHEUXWRZLQVWXLW JHGUXNWDOVSHUFHQWDJHYDQGH SULMV %UXWRZLQVWEHUHNHQLQJHQ ZRUGHQXLWJHGUXNWDOVSHUFHQW DJHYDQGHNRVWHQ

$OVXHHQYDQGHZDDUGHQZLOWEHNLMNHQGLHELMGHEHUHNHQLQJYDQPDUJH HQEUXWRZLQVWZRUGWJHEUXLNWGUXNWXRS HQYHUYROJHQVRSGHWRHWV GLHXZLOWEHNLMNHQ%LMYRRUEHHOGDOVXGHZDDUGHGLHLQ LVRSJHVODJHQ ZLOW]LHQGUXNWXRS 0DUJHHQEUXWRZLQVWKHEEHQKHW]HOIGH RSVODJUHJLVWHU$OVXRSVODDWLQ HQYHUYROJHQVRS GUXNW]LHW X

7

]

7

Margeberekeningen Voorbeeld. .LORZDWW(OHFWURQLFVNRRSWWHOHYLVLHVLQYRRU'H WHOHYLVLHVZRUGHQWHJHQYHUNRFKW+RHJURRWLVGHPDUJH" Toetsen:

7 c ]

Display:

Beschrijving:

255,00

6ODDWGHNRVWHQLQN RRSSULMV RSLQ&67 6ODDWGHYHUNRRSSULMV RSLQ35& %HUHNHQWGHPDUJH

300,00 15,00


35


Berekeningen van de brutowinst ten opzichte van de kosten Voorbeeld. 'HVWDQGDDUGEUXWRZLQVWRSNHWWLQJHQLVELM.OHLQHU·V

.RVPHWLTXH=LMKHEEHQHHQ]HQGLQJFKRNHUFROOLHUVRQWYDQJHQGLH SHUVWXNNRVWHQ:DWLVGHYHUNRRSSULMVSHUFKRNHU" Toetsen:

7 c

Display:

Beschrijving:

19,00

6ODDWGHNRVWHQRS 6ODDWGHEUXWRZLQVWRS %HUHNHQWGHYHUNRRS SULMV

60,00 30,40

Marge en brutowinst tegelijkertijd gebruiken Voorbeeld. (HQFR|SHUDWLHILQNRRSEXUHDXNRRSWNLVWHQPHWEOLNNHQ VRHSLQWHJHQHHQIDFWXXUSULMVYDQSHUNLVW$OVGHFR|SHUDWLH JHZRRQOLMNHHQEUXWRZLQVWYDQKDQWHHUWWHJHQZHONHSULMVPRHWHHQ NLVWVRHSEOLNNHQGDQZRUGHQYHUNRFKW"(QKRHJURRWLVGHPDUJH" Toetsen:

7 c ]

36

Display:

Beschrijving:

9,60

6ODDWGHLQNRRSNRVWHQ RS 6ODDWGHEUXWRZLQVWRS %HUHNHQWGHSULMVYDQ HHQNLVWVRHSEOLNNHQ %HUHNHQWGHPDUJH

15,00 11,04 13,04



3 Het opslaan van getallen en rekenkundige bewerkingen Het gebruik van opgeslagen getallen bij berekeningen 8NXQWRSYHUVFKLOOHQGHPDQLHUHQJHWDOOHQRSVODDQHQGH]HYHUYROJHQV RSQLHXZJHEUXLNHQ n *HEUXLN FRQVWDQW RPHHQJHWDOHQGHGDDUELMEHKRUHQGH RSHUDQGRSWHVODDQDOVXGLWYDDNZLOWJHEUXLNHQ n *HEUXLNJHKHXJHQWRHWVHQ HQ RPPHWppQ WRHWVDDQVODJJHWDOOHQRSWHVODDQWHODGHQHQELMHONDDURSWHWHOOHQ n *HEUXLN HQ RPJHWDOOHQRSWHVODDQLQRIWHODGHQXLWGH JHQXPPHUGHUHJLVWHUV

-

*!

a

Het gebruik van constanten

*HEUXLN RPHHQJHWDOHQHHQUHNHQNXQGLJHRSHUDWRU RSWHVODDQYRRUKHUKDOHQGHEHZHUNLQJHQ1DGDWGH FRQVWDQWHEHZHUNLQJLVRSJHVODJHQYRHUWXHHQJHWDOLQHQ GUXNWXRS 'HRSJHVODJHQEHZHUNLQJZRUGWXLWJHYRHUG PHWKHWJHWDOGDWLQGHGLVSOD\VWDDW

3: Het opslaan van getallen en rekenkundige bewerkingen

37


Toetsen

Bewerking

JHWDO - JHWDO - "JHWDO - dJHWDO - *^[ ZDDUGH -

JHWDO - JHWDO - "JHWDO - dJHWDO -

6ODDW´JHWDOµRSDOVHHQFRQVWDQWH 6ODDW´²JHWDOµRSDOVHHQFRQVWDQWH 6ODDW´ïJHWDOµRSDOVHHQFRQVWDQWH 6ODDW´¸JHWDOµRSDOVHHQFRQVWDQWH 6ODDW´\ µRSDOVHHQFRQVWDQWH 6ODDW´JHWDOµRSDOVHHQFRQVWDQWH [ZDDUGH

6ODDW´²JHWDOµRSDOVHHQFRQVWDQWH 6ODDW´ïJHWDOµRSDOVHHQFRQVWDQWH 6ODDW´¸JHWDOµRSDOVHHQFRQVWDQWH

Voorbeeld. %HUHNHQHQ Toetsen:

Display:

Beschrijving:

2,00

6ODDW´µRSDOVHHQ FRQVWDQWH

7,00

7HOWRS

8,00

7HOWRS

9,00

7HOWRS

Voorbeeld. %HUHNHQHQ

Toetsen:

38

Display:

Beschrijving:

1,00

6ODDW´µRSDOV HHQFRQVWDQWH 7HOWELMRS 7HOWELMRS 7HOWELMRS

11,00 12,10 27,50



Voorbeeld. %HUHNHQ HQ

*^ Toetsen:

Display:

Beschrijving:

3,00

6ODDW´\ µRSDOVHHQFRQVWDQWH

8,00

%HUHNHQW

64,00

%HUHNHQW

Het gebruik van het M-register

a

'H HQ WRHWVHQYRHUHQJHKHXJHQEHZHUNLQJHQ XLWRSHHQHQNHOYRXGLJRSVODJUHJLVWHUKHW0UHJLVWHU,QGH PHHVWHJHYDOOHQLVKHWQLHWQRGLJRPKHW0UHJLVWHUWH ZLVVHQDDQJH]LHQPHW GHUHHGVDDQZH]LJHLQKRXG ZRUGWYHUYDQJHQ8NXQWKHW0UHJLVWHUHFKWHUZLVVHQ GRRURS WHGUXNNHQ$OVXHHQDDQWDOJHWDOOHQDDQ KHW0UHJLVWHUWRHYRHJWNXQWX JHEUXLNHQRPKHW HHUVWHJHWDORSWHVODDQHQ RPGHYROJHQGHJHWDOOHQLQWHEUHQJHQ8 WUHNWKHWZHHUJHJHYHQJHWDOYDQKHWJHWDOLQKHW0UHJLVWHUDIGRRURS HQYHUYROJHQVRS WHGUXNNHQ

a

Toetsen

(

Beschrijving

6ODDWKHWZHHUJHJHYHQJHWDOLQKHW0UHJLVWHURS +DDOWKHWJHWDOXLWKHW0UHJLVWHURS 7HOWKHWZHHUJHJHYHQJHWDORSELMKHWLQJHWDOLQ KHW0UHJLVWHU

Voorbeeld. 7HOPHWEHKXOSYDQKHW0UHJLVWHUDQGELM

HONDDURS7UHNGDDUYHUYROJHQVYDQDIHQKDDOKHWUHVXOWDDWRS

( a Toetsen:

Display:

Beschrijving:

17,00

6ODDWLQKHW0UHJLVWHURS 7HOWELMKHW0UHJLVWHURS 7HOWELMKHW0UHJLVWHURS 7HOW²ELMKHW0UHJLVWHURS +DDOWGHLQKRXGYDQKHW0 UHJLVWHURS

14,25 16,95 –4,65 43,55


39


Het gebruik van genummerde registers

*! *!

0HWGH HQ WRHWVHQNULMJWXWRHJDQJWRWGH RSVODJUHJLVWHUV0HWGH WRHWVNRSLHHUWXKHW ZHHUJHJHYHQJHWDOQDDUHHQEHSDDOGUHJLVWHU0HWGH WRHWVNRSLHHUWXHHQJHWDOXLWHHQUHJLVWHUQDDUGHGLVSOD\

(HQJHWDORSVODDQRIRSYUDJHQLQWZHHVWDSSHQ 'UXNRS RI $OVXGH]HVWDSRQJHGDDQZLOWPDNHQGUXNW XRS RIRS 9RHUKHWQXPPHUYDQKHWUHJLVWHULQWRWHQPHW

R *!%

,QKHWYROJHQGHYRRUEHHOGZRUGHQWZHHRSVODJUHJLVWHUVJHEUXLNW %HUHNHQKHWYROJHQGH 475, 6 560, 1 + 475, 6 ---------------HQ ------------------------------------39, 15 39, 15

*! 6ODDWKHWZHHUJHJHYHQ JHWDO LQ5 RS d*! 6ODDWLQ5 RS +LHUPHHLVGHHHUVWHEHUHNHQLQJ DI 9UDDJW5 RS d 9UDDJW5 RS +LHUPHHLVGHWZHHGH EHUHNHQLQJDI 8NXQW*!HQRRNJHEUXLNHQYRRUWRHSDVVLQJVUHJLVWHUVPDDUQLHW ELMVWDWLVWLHN%LMYRRUEHHOGPHW*!.VODDWXKHWJHWDOGDWLQGH GLVSOD\VWDDWLQKHW.UHJLVWHURS0HW.NRSLHHUWXGHLQKRXGYDQ .QDDUGHGLVSOD\ Toetsen:

Display:

Beschrijving:

475,60

39,15

12,15

475,60

39,15

26,45

,QGHPHHVWHJHYDOOHQLVKHWQLHWQRGLJRPGHRSVODJUHJLVWHUVWHZLVVHQ RPGDWGRRUKHWRSVODDQYDQJHWDOOHQGHUHHGVDDQZH]LJHLQKRXGZRUGW YHUYDQJHQ8NXQWDI]RQGHUOLMNHUHJLVWHUVZLVVHQGRRUHULQRSWHVODDQ WHGUXNNHQ 8ZLVWDOOHUHJLVWHUVWHJHOLMNHUWLMGGRRURS

*&

40



Rekenkundige bewerkingen uitvoeren binnen een register 8NXQWLQGHRSVODJUHJLVWHUV5 WRWHQPHW5 UHNHQNXQGLJHEHZHUNLQJHQ XLWYRHUHQ+HWUHVXOWDDWZRUGWLQKHWUHJLVWHURSJHVODJHQ

Toetsen

Nieuw getal in register

*! U HJLVWHUQXPPHU *!U HJLVWHUQXPPHU *!"U HJLVWHUQXPPHU *!dU HJLVWHUQXPPHU

5HHGVDDQZH]LJHLQKRXGKHW ZHHUJHJHYHQJHWDO 5HHGVDDQZH]LJHLQKRXG²KHW ZHHUJHJHYHQJHWDO 5HHGVDDQZH]LJHLQKRXGïKHW ZHHUJHJHYHQJHWDO 5HHGVDDQZH]LJHLQKRXG¸KHW ZHHUJHJHYHQJHWDO

Voorbeeld. 6ODLQ5 RSYHUPHQLJYXOGLJGLWPHWHQVODKHW

UHVXOWDDWLQ5 RS

*! *!" Toetsen:

Display:

Beschrijving:

45,70

6ODDWLQ5 RS

2,50

9HUPHQLJYXOGLJW LQ5 PHWHQVODDW KHWUHVXOWDDW LQ 5 RS

114,25

*HHIW5 ZHHU


41


Rekenkundige bewerkingen uitvoeren :LVNXQGLJHIXQFWLHVZRUGHQRSKHWJHWDOLQGHGLVSOD\ XLWJHYRHUG

Voorbeeld. %HUHNHQ HQYHUYROJHQV

*[ *T

*h Toetsen:

Display:

Beschrijving:

0,25

%HUHNHQWGHUHFLSURTXH YDQ %HUHNHQW√ %HUHNHQW√

4,47 51,67 1,21

%HUHNHQW 'HEHZHUNLQJLVNODDU

52,88

Voorbeeld. %HUHNHQGHQDWXXUOLMNHORJDULWPHH

* *? Toetsen:

*e

42

%HUHNHQYHUYROJHQV

Display:

Beschrijving:

12,18

%HUHNHQWH %HUHNHQWGHQDW XXUOLMNHORJDULWPHYDQ KHWUHVXOWDDW %HUHNHQWIDFXOWHLW 'HEHZHUNLQJLVNODDU

2,50

24,00 814,00



Machtverheffingsoperator

*^

'HPDFKWYHUKHIILQJVRSHUDWRU YHUKHIWKHW YRRUJDDQGHJHWDO\ZDDUGH WRWGHPDFKWYDQKHW GDDURSYROJHQGHJHWDO[ZDDUGH

Voorbeeld. %HUHNHQ HQEHUHNHQYHUYROJHQVGHGHUGHPDFKWVZRUWHO

YDQ

*^ *^ *[ Toetsen:

Display:

Beschrijving:

1.953.125,00

%HUHNHQW %HUHNHQWGHGHUGH PDFKWVZRUWHOYDQ ZDWJHOLMNLVDDQ

5,00

Het gebruik van haakjes in berekeningen 'RRUKDDNMHVWHJHEUXLNHQNXQWXKHWEHUHNHQHQYDQHHQWXVVHQWLMGV UHVXOWDDWXLWVWHOOHQWRWGDWXPHHUJHWDOOHQKHEWLQJHYRHUG8NXQWWRWYLHU RSHQKDDNMHVJHEUXLNHQLQHONHEHUHNHQLQJ9HURQGHUVWHOGDWXKHW YROJHQGHZLOWEHUHNHQHQ

d

---------------------- × ( – )

LQYRHUWJHHIWGHFDOFXODWRUKHWWXVVHQWLMGVUHVXOWDDW $OVX ZHHU'LWUHVXOWDDWNULMJWXRPGDWEHUHNHQLQJHQZDDUJHHQKDDNMHVLQ VWDDQYDQOLQNVQDDUUHFKWVZRUGHQXLWJHYRHUGQHW]RDOVX]HLQYRHUW$OV XGHGHOLQJZLOWXLWVWHOOHQWRWGDWXYDQKHEWDIJHWURNNHQPRHWX KDDNMHVJHEUXLNHQ+HWVOXLWHQYDQGHKDDNMHVDDQKHWHLQGHYDQHHQ XLWGUXNNLQJNDQZRUGHQZHJJHODWHQ%LMYRRUEHHOGKHWLQYRHUHQYDQ´ ÷ï µLVJHOLMNDDQKHWLQYRHUHQYDQ´÷ï µ


43


Toetsen:

d* * "

44

Display:

Beschrijving:

85,00

(UZRUGWQRJQLHWV EHUHNHQG

73,00

%HUHNHQW²

0,41

%HUHNHQW÷

3,70

9HUPHQLJYXOGLJWKHW UHVXOWDDWPHW



4 Financiële problemen in beeld brengen Het benaderen van een financieel probleem 'HZRRUGHQVFKDWYDQGH+3%,,LVYHUHHQYRXGLJGRPDOOHILQDQFLsOH WHUPHQWHNXQQHQRPYDWWHQ+HWNDQ]LMQGDWELQQHQXZYDNJHELHGGH WHUPVDOGREDOORQEHWDOLQJUHVLGXZDDUGHYHUYDOZDDUGHRIXLWVWDDQGEHGUDJZRUGW JHEUXLNWRPHHQZDDUGHDDQWHJHYHQGLHGH+3%,,NHQWDOV WRHNRPVWLJHZDDUGH

/

'HYHUHHQYRXGLJGHWHUPLQRORJLHYDQGH+3%,,LVJHEDVHHUGRS FDVKIORZGLDJUDPPHQ&DVKIORZGLDJUDPPHQ]LMQILJXUHQYDQILQDQFLsOH YUDDJVWXNNHQZDDUELMGHFDVKIORZDOVIXQFWLHYDQGHWLMGZRUGWXLWJHGUXNW 'HHHUVWHVWDSQDDUKHWRSORVVHQYDQHHQILQDQFLHHOYUDDJVWXNLVKHW PDNHQYDQHHQFDVKIORZGLDJUDP ,QKHWFDVKIORZGLDJUDPGDWXKLHURQGHUYLQGW]LMQLQYHVWHULQJHQLQHHQ EHOHJJLQJVIRQGVZHHUJHJHYHQ'HRRUVSURQNHOLMNHLQYHVWHULQJZDV JHYROJGGRRULQYHVWHULQJHQYDQHQDDQKHW HLQGYDQGHGHUGHHQ]HVGHPDDQG$DQKHWHLQGYDQGHGHPDDQGZHUG RSJHQRPHQ$DQKHWHLQGYDQGHGHPDDQGZHUG RSJHQRPHQ

4: Financiële problemen in beeld brengen

45


16.567,20 Pijlen omhoog geven positieve cash flows aan (ontvangen geld).

5.000,00 De horizontale lijn geeft de tijd aan, verdeeld in regelmatige periodes.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Pijlen omlaag geven negatieve cash flows aan (betalingen).

-5.000,00

-6.000,00

-7.000,00

,HGHUFDVKIORZYRRUEHHOGNDQDOVHHQFDVKIORZGLDJUDPZRUGHQ ZHHUJHJHYHQ*HHIELMKHWPDNHQYDQHHQFDVKIORZGLDJUDPDDQZDWHU ZHORIQLHWEHNHQGLVRYHUGHWUDQVDFWLH 'HWLMGZRUGWZHHUJHJHYHQDOVHHQKRUL]RQWDOHOLMQGLHLQJHOLMNH WLMGVSHULRGHVLVYHUGHHOG&DVKIORZVZRUGHQDOV]LMYRRUNRPHQRSGH KRUL]RQWDOHOLMQJHSODDWVW:DDUJHHQSLMOHQ]LMQJHWHNHQG]LMQJHHQ FDVKIORZV

Het teken van de cashflow ,QFDVKIORZGLDJUDPPHQZRUGHQJHwQYHVWHHUGHEHGUDJHQDOVQHJDWLHIHQ RSJHQRPHQEHGUDJHQDOVSRVLWLHIDDQJHJHYHQ8LWJDDQGHEHGUDJHQ]LMQ QHJDWLHIHQELQQHQNRPHQGHEHGUDJHQ]LMQSRVLWLHI 9DQXLWKHWVWDQGSXQWYDQGHNUHGLHWJHYHULVFDVKIORZGLHDDQNODQWHQDOV OHQLQJZRUGWJHJHYHQQHJDWLHI2SGH]HOIGHZLM]HLVFDVKIORZGLHGH NUHGLHWYHUOHQHURQWYDQJWYDQ]LMQNODQWHQSRVLWLHI9DQXLWKHW JH]LFKWVSXQWYDQGHNUHGLHWQHPHUZRUGWKHWJHOHHQGHEHGUDJDOVSRVLWLHI JH]LHQWHUZLMOKHWWHUXJEHWDDOGHEHGUDJQHJDWLHILV

46



Periodes en cashflows %HKDOYHKHWWHNHQYDQKHWEHGUDJXLWJDDQGHFDVKIORZQHJDWLHIHQ LQNRPHQGHFDVKIORZSRVLWLHI PRHWHUELMFDVKIORZGLDJUDPPHQQRJPHHU LQDFKWZRUGHQJHQRPHQ n 'HWLMGOLMQLVLQJHOLMNHWLMGVLQWHUYDOOHQYHUGHHOG'HPHHVW YRRUNRPHQGHSHULRGHLVHHQPDDQGPDDUSHULRGHVYDQGDJHQ NZDUWDOHQHQMDUHQNRPHQRRNYDDNYRRU'HSHULRGHOLJWPHHVWDO YDVWLQHHQFRQWUDFWHQPRHWYRRUGDWXPHWXZEHUHNHQLQJEHJLQW EHNHQG]LMQ n $OVXHHQILQDQFLHHOYUDDJVWXNPHWGH+3%,,ZLOWRSORVVHQ PRHWHQDOOHFDVKIORZVDDQKHWEHJLQRIDDQKHWHLQGYDQHHQSHULRGH YRRUNRPHQ n $OVHUPHHUGDQppQFDVKIORZRSGH]HOIGHSODDWVLQKHW FDVKIORZGLDJUDPYRRUNRPWZRUGHQGLHELMHONDDURSJHWHOGRIYDQ HONDDUDIJHWURNNHQ%LMYRRUEHHOGHHQQHJDWLHYHFDVKIORZYDQ² HQHHQSRVLWLHYHFDVKIORZYDQNRPHQRSGH]HOIGH WLMGLQKHWFDVKIORZGLDJUDPYRRUHQZRUGHQDOVHHQFDVKIORZYDQ LQJHYRHUG² n (HQJHOGLJHILQDQFLsOHWUDQVDFWLHPRHWXLWWHQPLQVWHppQSRVLWLHYHHQ ppQQHJDWLHYHFDVKIORZEHVWDDQ

Enkelvoudige en samengestelde rente )LQDQFLsOHEHUHNHQLQJHQ]LMQJHEDVHHUGRSKHWIHLWGDWHURYHUHHQ EHSDDOGHSHULRGHUHQWHZRUGWEHWDDOGRYHUHHQVRPJHOG(U]LMQWZHH VRRUWHQUHQWHHQNHOYRXGLJHUHQWHHQVDPHQJHVWHOGHUHQWH'HEDVLVYRRU EHUHNHQLQJHQYDQGH7LPH9DOXHRI0RQH\HQGHFDVKIORZLVGH VDPHQJHVWHOGHUHQWH

Enkelvoudige rente %LMFRQWUDFWHQPHWHQNHOYRXGLJHUHQWHLVGHUHQWHHHQSHUFHQWDJHYDQGH RRUVSURQNHOLMNHKRRIGVRP'HUHQWHHQGHKRRIGVRP]LMQDDQKHWHLQG YDQKHWFRQWUDFWEHWDDOEDDU8OHHQWELMYRRUEHHOGYRRUHHQMDDUDDQ HHQYULHQGXLWHQXZLOWKLHUYRRUHQNHOYRXGLJHUHQWHKHEEHQ$DQ KHWHLQGYDQKHWMDDULVXZYULHQGXLVYDQ VFKXOGLJ (QNHOYRXGLJHUHQWHEHUHNHQLQJHQZRUGHQRSGH+3%,,PHWGH WRHWVXLWJHYRHUG(HQYRRUEHHOGYDQHHQHQNHOYRXGLJHUHQWHEHUHNHQLQJ YLQGWXRSSDJLQD

D


47


Samengestelde rente (HQFRQWUDFWPHWVDPHQJHVWHOGHUHQWHNXQWXEHVFKRXZHQDOVHHQDDQWDO DDQHHQJHVFKDNHOGHFRQWUDFWHQPHWHQNHOYRXGLJHUHQWH'HGXXUYDQLHGHU FRQWUDFWPHWHQNHOYRXGLJHUHQWHLVJHOLMNDDQppQSHULRGHELMGH VDPHQJHVWHOGHUHQWH$DQKHWHLQGYDQLHGHUHSHULRGHZRUGWGHUHQWHGLH EHWDDOGPRHWZRUGHQRYHULHGHUFRQWUDFWPHWHQNHOYRXGLJHUHQWHELMGH KRRIGVRPRSJHWHOG$OVXELMYRRUEHHOGRSHHQVSDDUUHNHQLQJ VWRUWPHWHHQMDDUOLMNVHUHQWHYDQGLHPDDQGHOLMNVZRUGWVDPHQJHVWHOG ZRUGWGHUHQWHEHUHNHQGDOVRIKHWRPHHQFRQWUDFWPHWHQNHOYRXGLJH UHQWHJDDWWHJHQó¸ $DQKHWHLQGYDQGHHHUVWHPDDQGLVKHW VDOGRYDQGHUHNHQLQJLVóYDQ ,QGHWZHHGHPDDQGYLQGWKHW]HOIGHSURFHVSODDWVRYHUKHWVDOGRYDQ +HWEHGUDJGDWDDQKHWHLQGYDQGHWZHHGHPDDQGZRUGW EHWDDOGLVóYDQRI'H]HFXPXODWLHZRUGWYRRUWJH]HW LQGHGHUGHYLHUGHHQYLMIGHPDDQG+HWWXVVHQWLMGVHUHVXOWDDWLQGH]H LOOXVWUDWLHLVRSGROODUVHQFHQWVDIJHURQG 1.005,00

1.010,03

1.015,08 1 1.020,16 2 1.025,26 3

4

-1.000,00

5

-1.005,00

-1.010,03

-1.015,08

-1.020,16

+HWZRRUGVDPHQJHVWHOGLQVDPHQJHVWHOGHUHQWHLVDIJHOHLGYDQGHJHGDFKWH GDWGHUHQWHGLHHHUGHUZHUGYHUGLHQGZRUGWWRHJHYRHJGDDQGH KRRIGVRP2SGH]HZLM]HEUHQJWKHWXLWVWDDQGHEHGUDJPHHURS'H PRJHOLMNKHGHQWRWKHWPDNHQYDQILQDQFLsOHEHUHNHQLQJHQRSGH+3 %,,]LMQJHEDVHHUGRSVDPHQJHVWHOGHUHQWH 48



De rentevoet $OVXHHQILQDQFLHHOSUREOHHPEHNLMNWPRHWX]LFKUHDOLVHUHQGDWGH UHQWHYRHWRIKHWUHQGHPHQWRSGULHPDQLHUHQNXQQHQZRUGHQ EHVFKUHYHQ n $OVSHULRGLHNHUHQWH'LWLVGHUHQWHGLHYDQSHULRGHWRWSHULRGHRYHU XZNDSLWDDOZRUGWEHUHNHQG n $OVHHQMDDUOLMNVHQRPLQDOHUHQWH'LWLVGHSHULRGLHNHUHQWH YHUPHQLJYXOGLJGPHWKHWDDQWDOSHULRGHVSHUMDDU n $OVMDDUOLMNVHHIIHFWLHYHUHQWH'LWLVHHQMDDUOLMNVHUHQWHYRHWZDDUELM FXPXODWLHLQDDQPHUNLQJZRUGWJHQRPHQ ,QKHWYRULJHYRRUEHHOGYDQHHQVSDDUUHNHQLQJYDQLVGH SHULRGLHNHUHQWHóSHUPDDQG XLWJHGUXNWDOVHHQMDDUOLMNVHQRPLQDOH UHQWHYDQóï 'H]HOIGHSHULRGLHNHUHQWHNDQRRNZRUGHQ XLWJHGUXNWDOVHHQMDDUOLMNVHHIIHFWLHYHUHQWHKHWVDOGRQDFXPXODWLHYDQ PDDQGHQLVZDWQHHUNRPWRSHHQMDDUOLMNVHHIIHFWLHYHUHQWH YDQ 9RRUEHHOGHQYDQKHWRP]HWWHQYDQQRPLQDOHQDDUMDDUOLMNVHHIIHFWLHYH UHQWHYLQGWXRSSDJLQD·VWRWHQPHW

Twee verschillende financiële vraagstukken 'HILQDQFLsOHYUDDJVWXNNHQLQGH]HKDQGOHLGLQJEHWUHIIHQVDPHQJHVWHOGH UHQWHWHQ]LMH[SOLFLHWLVDDQJHJHYHQGDWKHWRPYUDDJVWXNNHQPHW HQNHOYRXGLJHUHQWHJDDW)LQDQFLsOHYUDDJVWXNNHQZRUGHQLQWZHHJURHSHQ YHUGHHOG790YUDDJVWXNNHQHQFDVKIORZYUDDJVWXNNHQ

Het herkennen van een TVM-vraagstuk $OVWXVVHQGHHHUVWHHQGHODDWVWHSHULRGHYDQKHWFDVKIORZGLDJUDP XQLIRUPHFDVKIORZVRSWUHGHQLVKHWILQDQFLsOHYUDDJVWXNHHQ790 SUREOHHP790VWDDWYRRUZDDUGHYDQJHOGLQGHWLMG %LMGHRSORVVLQJ YDQ790YUDDJVWXNNHQVSHOHQGHYROJHQGHYLMIWRHWVHQHHQEHODQJULMNH URO


49


P . 2 /

$DQWDOSHULRGHVRIEHWDOLQJHQ -DDUOLMNVHUHQWHYRHWJHZRRQOLMNGHMDDUOLMNVHQRPLQDOHUHQWH +XLGLJHZDDUGHGHFDVKIORZDDQKHWEHJLQYDQGHWLMGOLMQ 3HULRGLHNHEHWDOLQJ 7RHNRPVWLJHZDDUGHGHFDVKIORZDDQKHWHLQGYDQKHWFDVKIORZ GLDJUDPRSJHWHOGELMSHULRGLHNHEHWDOLQJHQ

1DGDWXYLHUZDDUGHQKHEWLQJHYRHUGNXQWXGHDQGHUHZDDUGHEHUHNHQHQ &DVKIORZGLDJUDPPHQYRRUOHQLQJHQK\SRWKHNHQOHDVHV VSDDUUHNHQLQJHQRILHGHUFRQWUDFWRSEDVLVYDQUHJHOPDWLJHFDVKIORZVYDQ GH]HOIGHJURRWWHZRUGHQJHZRRQOLMNDOV790YUDDJVWXNNHQEHKDQGHOG +LHURQGHUYLQGWXHHQFDVKIORZGLDJUDPYDQHHQNUHGLHWQHPHUYRRUHHQ MDULJHK\SRWKHHNYDQPHWEHWDOLQJHQYDQWHJHQ MDDUOLMNVHUHQWHPHWHHQDIEHWDOLQJYDQYDQGHKRRIGVRP EDOORQEHWDOLQJ

PV = 150.000,00

I/YR = 7,5% 1

2

3

4

5

...

PMT = -1.041,40

N = 360 (30 × 12) 357 358 359 360

FV = -10.000,00

(pQYDQGHZDDUGHQYDQ39307)9 NDQJHOLMNDDQQXO]LMQ+LHURQGHU ]LHWXHHQFDVKIORZGLDJUDPYDQXLWKHWVWDQGSXQWYDQGHVSDDUGHU YRRU HHQVSDDUUHNHQLQJPHWHHQHHQPDOLJGHSRVLWRHQHHQHHQPDOLJHRSQDPH YLMIMDDUODWHU'HUHQWHZRUGWPDDQGHOLMNVVDPHQJHVWHOG,QGLWYRRUEHHOG LV307 JHOLMNDDQQXO

50



1

2

3 4 5

I/YR = 8,00% PMT = 0,00

...

FV = 25.327,38 56 57 58 59

60 N = 60

PV = -17.000,00 790EHUHNHQLQJHQZRUGHQLQKHWYROJHQGHKRRIGVWXNEHKDQGHOG

Het herkennen van een cashflowvraagstuk (HQILQDQFLHHOYUDDJVWXNZDDUELMJHHQVSUDNHLVYDQUHJHOPDWLJH XQLIRUPHEHWDOLQJHQVRPVRQHYHQFDVKIORZVJHQRHPG LVHHQ FDVKIORZYUDDJVWXNHQJHHQ790YUDDJVWXN +LHURQGHUYLQGWXHHQFDVKIORZGLDJUDPYRRUHHQLQYHVWHULQJLQHHQ EHOHJJLQJVIRQGV'LWLVHHQYRRUEHHOGYDQHHQYUDDJVWXNGDWRIPHW QHWWRKXLGLJHZDDUGH RIPHW LQWHUQMDDUOLMNVUHQGHPHQW ZRUGWRSJHORV

*N

*9


51


16.567,20

5.000,00

1

2

3

4

5

6

7

8

9

10

11

12

13

14

-5.000,00

-6.000,00

-7.000,00

&DVKIORZYUDDJVWXNNHQZRUGHQEHVFKUHYHQLQKRRIGVWXN

52


15

16


5 “Time Value of Money”berekeningen Het gebruik van de TVM-functie 'H790IXQFWLHZRUGWJHEUXLNWELMGHEHUHNHQLQJYDQ VDPHQJHVWHOGHUHQWHZDDUELMVSUDNHLVYDQXQLIRUPH FDVKIORZVGLHZHEHWDOLQJHQQRHPHQ1DGDWGHZDDUGHQ ]LMQLQJHYRHUGNXQWXWHONHQVppQZDDUGHYDULsUHQ]RQGHU DOOHZDDUGHQRSQLHXZLQWHYRHUHQ (UPRHWDDQEHSDDOGHYRRUZDDUGHQZRUGHQYROGDDQRPGH790IXQFWLH WHNXQQHQJHEUXLNHQ n +HWEHGUDJYDQLHGHUHEHWDOLQJPRHWJHOLMN]LMQ$OVGHJURRWWHYDQGH EHWDOLQJHQYDULHHUWPRHWXGHZHUNZLM]HYROJHQGLHEHVFKUHYHQVWDDW LQKRRIGVWXN´&DVKIORZEHUHNHQLQJHQµ n %HWDOLQJHQPRHWHQPHWUHJHOPDWLJHWXVVHQSR]HQJHGDDQZRUGHQ n 'HEHWDOLQJVSHULRGHPRHWVDPHQYDOOHQPHWGHSHULRGHZDDURYHUGH VDPHQJHVWHOGHUHQWHZRUGWEHUHNHQG,VGLWQLHWKHWJHYDOYHUDQGHU GDQGHUHQWHYRHWPHWGHWRHWVHQ HQ ]RDOVGDW RSSDJLQD ZRUGWEHVFKUHYHQ n (UPRHWWHQPLQVWHppQSRVLWLHYHHQppQQHJDWLHYHFDVKIORZ YRRUNRPHQ

* *Z *b

5: “Time Value of Money”-berekeningen

53


P .

Toets

2 / *b *U *O * /

Slaat op of berekent

+HWDDQWDOEHWDOLQJHQRIFXPXODWLHYHSHULRGHV 'HMDDUOLMNVHQRPLQDOHUHQWHYRHW 'HKXLGLJHZDDUGHYDQWRHNRPVWLJHFDVKIORZV39 LVJHZRRQOLMNHHQHHUVWHLQYHVWHULQJRIHHQJHOHHQG EHGUDJHQNRPWDOWLMGDDQKHWEHJLQYDQGHHHUVWH SHULRGHYRRU +HWEHGUDJYDQGHSHULRGLHNHEHWDOLQJHQ$OOH EHWDOLQJHQ]LMQHYHQJURRWHQHUZRUGWJHHQHQNHOH RYHUJHVODJHQEHWDOLQJHQNXQQHQDDQKHWEHJLQRI DDQKHWHLQGYDQGHSHULRGHJHGDDQZRUGHQ 'HWRHNRPVWLJHZDDUGH)9LVRIHHQODDWVWHFDVK IORZRIGHVDPHQJHVWHOGHZDDUGHYDQHHQUHHNVHHU GHUHFDVKIORZV)9NRPWDDQKHWHLQGYDQGH ODDWVWHSHULRGHYRRU 6ODDWKHWDDQWDOSHULRGHVSHUMDDURS'HVWDQGDDUG ZDDUGHLV6WHOGLWDOOHHQRSQLHXZLQDOVXHHQ YHUDQGHULQJZLOWDDQEUHQJHQ'H]HWRHWVEHYLQGW ]LFKRQGHUGH WRHWV

2

2SWLRQHOHYHUNRUWHPDQLHUYRRUKHWLQYRHUHQYDQ 1KHWJHWDOLQGHGLVSOD\ZRUGWYHUPHQLJYXOGLJG PHWGHZDDUGHLQ3<5HQKHWUHVXOWDDWZRUGWLQ1 RSJHVODJHQ'H]HWRHWVYLQGWXRQGHUGH WRHWV

P

:LVVHOWWXVVHQGH%HJLQHQ(LQGPRGXV,QGH %HJLQPRGXV]LHWXGHBEGIN LQGLFDWRU %HUHNHQWHHQDIEHWDOLQJVWDEHO

P . 2 *U *b

8NXQWZDDUGHQYHULILsUHQGRRURS HQ WHGUXNNHQ$OVXRS GUXNWZRUGWKHWWRWDDODDQWDO EHWDOLQJHQJHGXUHQGHDOOHMDUHQJHWRRQGHQDOVXRS GUXNW ZRUGWKHWDDQWDOEHWDOLQJHQSHUMDDURSJHURHSHQ+HWRSYUDJHQYDQGH]H JHWDOOHQYHUDQGHUWGHLQKRXGYDQGHUHJLVWHUVQLHW

54



TVM-registers wissen

*&

'RRURS WHGUXNNHQZLVWXDOOH790UHJLVWHUV+LHUGRRUNULMJHQ 1,<539307HQ)9GHZDDUGHQXO'HKXLGLJHZDDUGHYDQ3<5 YHUVFKLMQWNRUWLQGHGLVSOD\

Begin- en Eindmodus 9RRUGDWXDDQHHQ790EHUHNHQLQJEHJLQWPRHWX DDQJHYHQRIGHHHUVWHSHULRGLHNHEHWDOLQJDDQKHWEHJLQRI DDQKHWHLQGYDQGHHHUVWHSHULRGHYRRUNRPW$OVGHHHUVWH EHWDOLQJDDQKHWHLQGYDQGHHHUVWHSHULRGHJHEHXUWPRHW XGH+3%,,RS(LQGPRGXVLQVWHOOHQ$OVGH]HDDQKHW EHJLQYDQGHHHUVWHSHULRGHYRRUNRPWGDQVWHOWXGH FDOFXODWRURSGH%HJLQPRGXVLQ

*O

WH 8NXQWWXVVHQ%HJLQHQ(LQGPRGXVRPVFKDNHOHQGRRURS GUXNNHQ$OVGHFDOFXODWRULQGH%HJLQPRGXVLV]LHWXGHBEGIN LQGLFDWRU8]LHWJHHQLQGLFDWRUDOVXLQGH(LQGPRGXVEHQW +\SRWKHNHQHQOHQLQJHQJHEUXLNHQPHHVWDOGH(LQGPRGXV /HDVHFRQWUDFWHQHQVSDDUSODQQHQJHEUXLNHQRYHUKHWDOJHPHHQGH %HJLQPRGXV

Het berekenen van leningen Voorbeeld: Een autolening. 8ILQDQFLHUWHHQDXWRPHWHHQOHQLQJYDQ GULHMDDUWHJHQMDDUOLMNVHQRPLQDOHUHQWHPDDQGHOLMNVVDPHQJHVWHOG 'HDXWRNRVW8EHWDDOWYRRUXLW Deel 1. :DW]LMQXZPDDQGHOLMNVHEHWDOLQJHQELMHHQUHQWHYDQ" 1HHPDDQGDWXHHQPDDQGQDGHDDQNRRSRIDDQKHWHLQGYDQGHHHUVWH SHULRGHEHJLQWPHWGHDIEHWDOLQJHQ


55


PV = 14.500 - 1.500 I/YR = 10,5% N = 3 × 12 P/YR = 12 1

...

2 PMT = ? Eindmodus

6WHOGH(LQGPRGXVLQ'UXNRS

*b "P . / 2 Toetsen:

56

*O

35

36


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOSHUL RGHVSHUMDDULQ 6ODDWKHWDDQWDO SHULRGHVYDQGHOHQLQJ RS 6ODDWGHMDDUOLMNVH QRPLQDOHUHQWHYRHWRS 6ODDWKHWJHOHHQGH EHGUDJRS 6ODDWKHWEHGUDJRSGDW QRJXLWVWDDWQDGULHMDDU %HUHNHQWGHPDDQ GHOLMNVHDIEHWDOLQJ+HW PLQWHNHQJHHIWKHW EHWDDOGHEHGUDJDDQ

36,00

10,50 13.000,00 0,00 –422,53



Deel 2. %LMZHONHUHQWHYRHWZRUGWKHWPDDQGHOLMNVWHEHWDOHQEHGUDJPHW YHUPLQGHUGWRWELMHHQKRRIGVRPYDQ"

2 .

9HUPLQGHUWGHEHWDOLQJ WRYGHHHUGHUEHUHN HQGH %HUHNHQWGHMDDUOLMNVH UHQWHYRHWYRRUGH JHUHGXFHHUGHEHWDOLQJ

–372,53

2,03

Deel 3. $OVGHUHQWHLVHQXSHUPDDQGQLHWPHHUGDQZLOW EHWDOHQZDWNXQWXGDQPD[LPDDODDQHHQQLHXZHDXWRXLWJHYHQ"

. (2

10,50

–375,00 11.537,59 13.037,59

6ODDWGHRRU VSURQNHOLMNHUHQWHYRHW RS 6ODDWGHJHZHQVWH EHWDOLQJRS %HUHNHQWKHWWHILQDQ FLHUHQEHGUDJ 7HOWGHYRRUXLWEHWDOLQJ RSELMKHWJHILQDQFLHUGH EHGUDJRPGHWRWDOH SULMVYDQGHDXWRWHNULM JHQ

Voorbeeld: Een hypotheek op een huis. 8YLQGWGDWKHWPD[LPDOH PDDQGHOLMNVHEHGUDJGDWXDDQHHQK\SRWKHHNNXQWXLWJHYHQLV8 NXQWHHQYRRUXLWEHWDOLQJPDNHQYDQHQGHMDDUOLMNVHUHQWHYRHWLV RSKHWRJHQEOLN$OVXHHQK\SRWKHHNYRRUMDDUNXQWNULMJHQZDW LVGDQGHPD[LPDOHDDQNRRSSULMVGLHX]LFKNXQWYHURRUORYHQ"


57


PV = ? I/YR = 7,5% N = 30 × 12 P/YR = 12 1

2

3

...

4

PMT = -930,00 Eindmodus 6WHOGH(LQGPRGXVLQ'UXNRS

*b *U / . (2 Toetsen:


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOSHUL RGHVSHUMDDULQ 6WHOWGHGXXUYDQGH K\SRWKHHNLQï %HWDDOWGHK\SRWKHHNLQ MDDUDI 6ODDWGHUHQWHYRHWRS 6ODDWGHJHZHQVWH EHWDOLQJRSXLWEH WDDOGHEHGUDJLV QHJDWLHI %HUHNHQWKRHJURRWGH OHQLQJLVELMPDDQ GHOLMNVHEHWDOLQJHQYDQ 7HOWDDQ YRRUXLWEHWDOLQJRSRP GHWRWDOHDDQNRRSSULMV WHNULMJHQ

360,00 0,00 7,50 –930,00

133.006,39

58

*O

356 357 358 359 360

145.006,39



Voorbeeld: Een hypotheek met een ballonbetaling. 8KHEWHHQ K\SRWKHHNYDQJHNUHJHQYRRUMDDUWHJHQHHQMDDUOLMNVH UHQWHYRHWYDQ8YRRU]LHWGDWXKHWKXLVQDYLHUMDDU]XOWYHUNRSHQ HQGHOHQLQJPHWHHQEDOORQEHWDOLQJ]XOWWHUXJEHWDOHQ:DW]DOGH EDOORQEHWDOLQJ]LMQ"

/RVGLWSUREOHHPRSLQWZHHHWDSSHV %HUHNHQGHEHWDOLQJRSGHOHQLQJRSEDVLVYDQHHQWHUPLMQYDQ MDDU %HUHNHQKHWRYHUEOLMYHQGHVDOGRQDYLHUMDDU Punt 1. %HUHNHQHHUVWGHEHWDOLQJRSGHOHQLQJJHEDVHHUGRSHHQWHUPLMQ YDQMDDU

PV = 172.500 I/YR = 8,8% N = 25 × 12 P/YR = 12 1

...

2 PMT = ? Eindmodus


*b *U / . 2 Toetsen:

*O

299

300


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOSHULRGHVSHUMDDU LQ 6ODDWGHGXXUYDQGHK\SRWKHHN RSï PDDQGHQ 6ODDWKHWVDOGRYDQGHOHQLQJQD MDDURS 6ODDWKHWVDOGRYDQGH RRUVSURQNHOLMNHOHQLQJRS 6ODDWGHMDDUOLMNVHUHQWHYRHWRS %HUHNHQWGHPDDQGHOLMNVH DIEHWDOLQJ

300,00 0,00 172.500,00 8,80 –1.424,06


59


Punt 2. $DQJH]LHQGHEHWDOLQJDDQKHWHLQGYDQGHPDDQGZRUGWJHGDDQ ZRUGHQGHODDWVWHEHWDOLQJHQGHEDOORQEHWDOLQJWHJHOLMNHUWLMGJHGDDQ'H ODDWVWHEHWDOLQJLVGHVRPYDQ307HQ)9

PV = 172.500,00 I/YR = 8,8% N = 4 × 12 P/YR = 12 1

2

3

...

4

44 45 46 47 48

PMT = -1.424,06 Eindmodus

FV = ?

'HZDDUGHLQ307PRHWELMKHWEHUHNHQHQYDQ)9RI39 DOWLMGRSWZHHGHFLPDOHQDIJHURQGZRUGHQRPNOHLQH]LFK FXPXOHUHQGHYHUVFKLOOHQWXVVHQQLHWDIJHURQGHHQ ZHUNHOLMNHGROODUVHQFHQWV EHWDOLQJHQWHYHUPLMGHQ$OV GHGLVSOD\QLHWRSWZHHGHFLPDOHQLVLQJHVWHOGGUXNWXRS

*

*L2 P /

2 Toetsen:

60

Display:

Beschrijving:

–1.424,06

5RQGWEHWDOLQJHQRSWZHH GHFLPDOHQDIHQVODDWGH]H GDQRS 6ODDWGHWHUPLMQYDQYLHUMDDU ï GLHXYHUZDFKWKHW KXLVWHEH]LWWHQRS %HUHNHQWKHWVDOGRYDQGH OHQLQJQDYLHUMDDU %HUHNHQWKHWWRWDDOYDQGHH EHWDOLQJ307HQ)9 YRRU KHWDIORVVHQYDQGHOHQLQJ KHWWHEHWDOHQEHGUDJZRUGW DDQJHGXLGDOVHHQQHJDWLHI JHWDO

48,00

–163.388,39 –164.812,45



Berekeningen met spaarsystemen Voorbeeld: Een spaarrekening. $OVXRSHHQVSDDUUHNHQLQJ VWRUWZDDUXHHQMDDUOLMNVHUHQWHYRHWYDQNULMJWHQYHUGHUJHHQDQGHUH EHGUDJHQVWRUWKRHODQJGXXUWKHWYRRUGDWHURSGHUHNHQLQJ VWDDW"

FV = 3.000,00 I/YR = 7,2% N=? P/YR = 1 1

2

3

...

N=?

PMT = 0 PV = -2.000,00 $DQJH]LHQHUJHHQUHJHOPDWLJHEHWDOLQJHQZRUGHQJHGDDQ307 LV GHEHWDOLQJVPRGXV(LQGRI%HJLQ QLHWYDQEHODQJ

*& *b ( / . P Toetsen: 1

Display:

Beschrijving:

0,00

:LVWDOOHUHJLVWHUV 6WHOW3<5JHOLMNDDQ DDQJH]LHQGHUHQWHMDDUOLMNV ZRUGWVDPHQJHVWHOG 6ODDWKHWEHGUDJRSYDQKHW HHUVWHGHSRVLWR 6ODDWKHWEHGUDJRSGDWXZLOW ELMHHQVSDUHQ 6ODDWGHMDDUOLMNVHUHQWHYRHW RS %HUHNHQWKHWDDQWDOMDUHQGDW QRGLJLVRPRSWH NRPHQ

1,00

–2.000,00 3.000,00 7,20 5,83


61


$DQJH]LHQGHEHUHNHQGHZDDUGHYDQ1WXVVHQHQOLJW]LMQHU WHQPLQVWH]HVMDUHQMDDUOLMNVHDFFXPXODWLHQRGLJRPRSWHQPLQVWHWH NRPHQ%HUHNHQKHWZHUNHOLMNHVDOGRQD]HVMDDU

P /

P

6WHOW RSMDDULQ %HUHNHQWKHWEHGUDJ GDWXQDMDDUNXQW RSQHPHQ

6,00 3.035,28

Voorbeeld: Een persoonlijke pensioenrekening. 8KHEWRSDSULO

HHQSHUVRRQOLMNHSHQVLRHQUHNHQLQJJHRSHQGHQGDDURS JHVWRUW(UZRUGWDIJHKRXGHQYDQXZORRQHQXZRUGWWZHHPDDO SHUPDDQGXLWEHWDDOG2SGHUHNHQLQJZRUGWMDDUOLMNVUHQWHEHWDDOG GLHSHUKDOYHPDDQGZRUGWJHDFFXPXOHHUG+RHYHHO]DOHURSDSULO RSGHUHNHQLQJVWDDQ"

FV= ?

(Halfmaandelijkse periodes) 1 2 3 4

I/YR = 6,3% N = 360 (15 jaar × 24 halve maanden) P/YR = 24

...

360

PMT = -80,00 PV = -2.000,00 6WHOGH(LQGPRGXVLQ'UXNRS

62

*O




*b ( (2 . *U / Toetsen:

Display:

Beschrijving:

24,00

6WHOWKHWDDQWDOSHULRGHVSHU MDDULQ 6ODDWGHHHUVWHVWRUWLQJRS 6ODDWGHUHJHOPDWLJH KDOIPDDQGHOLMNVHVWRUWLQJHQ RS 6ODDWGHUHQWHYRHWRS 6ODDWKHWDDQWDOVWRUWLQJHQRS %HUHNHQWKHWWHJRHG

–2.000,00 –80,00

6,30 360,00 52.975,60

Voorbeeld: Een annuïteitenrekening. 1DHHQVXFFHVYROOH ]DNHQFDUULqUHEHVOXLWXWHJDDQUHQWHQLHUHQ8KHEWJHVSDDUG ZDDURYHUXHHQJHPLGGHOGHMDDUOLMNVHUHQWHYDQNULMJWGLHPDDQGHOLMNV ZRUGWVDPHQJHVWHOG+RHJURRWLVKHWEHGUDJGDWXDDQKHWHLQGYDQ LHGHUHPDDQGNXQWRSQHPHQDOVXZLOWGDWXZVSDDUUHNHQLQJXJHGXUHQGH GHYROJHQGHMDDURQGHUVWHXQW"

PMT = ? 1

...

2

I/YR = 7% N = 600 (50 × 12) P/YR = 12 PV = -400.000,00 Beginmodus 6WHOGH%HJLQPRGXVLQ'UXNRS

*O

599

600 FV = 0

DOVXGHLQGLFDWRUQLHW]LHW


63


*b ( . *U / 2 Toetsen:

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ JHQSHUMDDULQ 6ODDWXZDSSHOWMHYRRU GHGRUVWDOVHHQXLW JDDQGHGHSRVLWRRS 6ODDWGHMDDUOLMNVHUHQW HYRHWRSGLHXGHQNWWH NULMJHQ 6ODDWKHWDDQWDO RSQDPHVRS 6ODDWKHWWHJRHGQD MDDURS %HUHNHQWKHWEHGUDJ GDWXDDQKHWEHJLQYDQ LHGHUHPDDQGNXQW RSQHPHQ

–400.000,00

7,00

600,00 0,00 2.392,80

Leaseberekeningen (HQOHDVHLVHHQOHQLQJYDQZDDUGHYROOHJRHGHUHQ]RDOVYDVWJRHGDXWR·V RIJHUHHGVFKDS JHGXUHQGHHHQEHSDDOGHWLMGWHJHQUHJHOPDWLJH EHWDOLQJHQ6RPPLJHOHDVHFRQWUDFWHQZRUGHQXLWJHVFKUHYHQDOV NRRSDNWHVPHWHHQRSWLHRPDDQKHWHLQGHYDQGHOHDVHSHULRGHWHNRSHQ VRPVYRRUDPSHU 'HYDVWJHVWHOGHWRHNRPVWLJHZDDUGH)9 YDQ GHJRHGHUHQDDQKHWHLQGYDQHHQOHDVHZRUGWVRPVGH´UHVLGXZDDUGHµRI ´XLWNRRSZDDUGHµJHQRHPG $OOHYLMI790WRHSDVVLQJVWRHWVHQNXQQHQELMOHDVHEHUHNHQLQJHQJHEUXLNW ZRUGHQ(U]LMQWZHHDOJHPHHQYRRUNRPHQGHOHDVHEHUHNHQLQJHQ n +HWEHUHNHQHQYDQGHOHDVHEHWDOLQJRPHHQEHSDDOGHRSEUHQJVWWH YHUNULMJHQ n +HWEHUHNHQHQYDQGHKXLGLJHZDDUGHJHNDSLWDOLVHHUGHZDDUGH YDQ HHQOHDVH 'HHHUVWHEHWDOLQJYRRUHHQOHDVHJHEHXUWJHZRRQOLMNDDQKHWEHJLQYDQGH HHUVWHSHULRGH'DDURPZRUGWHUELMGHPHHVWHOHDVHEHUHNHQLQJHQLQGH %HJLQPRGXVJHZHUNW

64



Voorbeeld: Het berekenen van een leasebetaling. (HQNODQWZLO

YRRUHHQDXWRHHQOHDVHRYHUHHQNRPVWYDQRYHUGULHMDDUDIVOXLWHQ 'HRYHUHHQNRPVWRPYDWHHQRSWLHRPGHDXWRDDQKHWHLQGYDQGH OHDVHSHULRGHWHNRSHQWHJHQ'HHHUVWHPDDQGHOLMNVHEHWDOLQJLV EHWDDOEDDURSGHGDJGDWGHNODQWLQJHEUXLNQHHPW$OVXHHQMDDUOLMNVH RSEUHQJVWYDQPDDQGHOLMNVVDPHQJHVWHOGZLOWKHEEHQZDW]LMQGDQ GHEHWDOLQJHQ"%HUHNHQGHEHWDOLQJYDQXLWXZVWDQGSXQWDOVGHDOHU

FV = 7.500,00 Door dealer ontvangen geld is positief

PMT = ? 1

2

...

35

I/YR = 10% N = 36 P/YR = 12

36 Door dealer uitgegeven geld is negatief

PV = -13.500,00 Beginmodus 6WHOGH%HJLQPRGXVLQ'UXNRS

*b . ( / P 2 Toetsen:

*O


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ JHQSHUMDDULQ 6ODDWGHJHZHQVWHMDDU OLMNVHRSEUHQJVWRS 6ODDWGHOHDVHSULMVRS 6ODDWGHUHVLGXZDDUGH XLWNRRSZDDUGH RS 6ODDWGHGXXUYDQGH OHDVHLQPDDQGHQRS %HUHNHQWGHPDDQ GHOLMNVHEHWDOLQJHQ

10,00 –13.500,00 7.500,00 36,00 253,99


65


8]LHWGDW]HOIVDOVGHNODQWGHDXWRQLHWZHQVWWHNRSHQHUDDQKHWHLQG YDQGHOHDVHHHQFDVKIORZELQQHQNRPWGLHJHOLMNLVDDQGHUHVLGXZDDUGH YDQGHDXWR2IGHNODQWGHDXWRQXNRRSWRIGDWGHDXWRRSGHYULMH PDUNWZRUGWYHUNRFKWGHOHDVHJHYHUYHUZDFKWHHQRSEUHQJVWYDQ Voorbeeld: Lease met vooruitbetalingen. 8ZEHGULMI.ZLN7LPPHU

ZLOHHQYRUNKHIWUXFNOHDVHQYRRUGHRSVODJSODDWV'HOHDVHZRUGW RSJHPDDNWYRRUHHQWHUPLMQYDQMDDUPHWPDDQGHOLMNVHEHWDOLQJHQYDQ %HWDOLQJHQZRUGHQDDQKHWEHJLQYDQGHPDDQGEHWDDOEDDUJHVWHOG HQGHHHUVWHHQODDWVWHEHWDOLQJPRHWHQELMKHWLQJDDQYDQGHOHDVH YHUUHNHQGZRUGHQ8KHEWGHRSWLHRPDDQKHWHLQGYDQGHOHDVHSHULRGH GHYRUNKHIWUXFNWHNRSHQWHJHQ $OVGHMDDUOLMNVHUHQWHYRHWLVZDWLVGDQGHJHNDSLWDOLVHHUGHZDDUGH YDQGHOHDVH"

Beginmodus PV = ? I/YR = 9% N = 48 P/YR = 12 1

2

3

4

...

44 45 46 47 48

PMT = -2.400,00 (48ste betaling vooruit) FV = -15.000,00 'H]HEHUHNHQLQJZRUGWLQYLHUVWDSSHQRSJHORVW %HUHNHQGHKXLGLJHZDDUGHYDQGHPDDQGHOLMNVHDIEHWDOLQJHQ ï ² 7HOGDDUELMGHZDDUGHYDQGHH[WUDYRRUXLWEHWDOLQJRS %HUHNHQGHKXLGLJHZDDUGHYDQGHNRRSRSWLH 7HOGHZDDUGHQXLWSXQWHQELMHONDDURS

66



Punt 1%HUHNHQGHKXLGLJHZDDUGHYDQGHPDDQGHOLMNVHDIEHWDOLQJHQ

6WHOGH%HJLQPRGXVLQ'UXNRS

*b P (2 / . Toetsen:

2(

*O


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ JHQSHUMDDULQ 6ODDWKHWDDQWDO EHWDOLQJHQRS 6ODDWGHPDDQGHOLMNVH EHWDOLQJRS 6ODDW)9YRRUSXQW RS 6ODDWGHUHQWHYRHWRS %HUHNHQWGHKXLGLJH ZDDUGHYDQGH PDDQGHOLMNVHEHWDOLQ JHQ

47,00 –2.400,00 0,00 9,00 95.477,55

Punt 2. 7HOGHH[WUDYRRUXLWEHWDOLQJELM39RS6ODKHWUHVXOWDDWRS

P 2 (/

97.877,55 97.877,55

7HOWGHH[WUDYRRUXLWEH WDOLQJRS 6ODDWKHWUHVXOWDDWLQ KHW0UHJLVWHURS

Punt 3. %HUHNHQGHKXLGLJHZDDUGHYDQGHNRRSRSWLH 48,00

0,00

–15.000,00

10.479,21

6ODDWGHPDDQGRS ZDQQHHUGHNRRSRSWLH ZRUGWXLWJHYRHUG 6ODDWHHQEHWDOLQJYDQ QXORSYRRUGLWSXQW YDQGHRSORVVLQJ 6ODDWGHZDDUGHRSGLH YHUGLVFRQWHHUGPRHW ZRUGHQ %HUHNHQWGHKXLGLJH ZDDUGHYDQGHODDWVWH FDVKIORZ


67


Punt 4. 7HOGHUHVXOWDWHQYDQSXQWHQELMHONDDURS

a

Toetsen:

Display:

Beschrijving:

108.356,77

%HUHNHQWGHKXLGLJH JHNDSLWDOLVHHUGH ZDDUGHYDQGHOHDVH $IURQGLQJVYHUVFKLOOHQ ZRUGHQRSSDJLQD YHUNODDUG

Amortisatie $PRUWLVDWLHLVKHWYHUGHOHQYDQKHWEHGUDJYDQHHQ EHWDOLQJLQHHQJHGHHOWHGDWEHWUHNNLQJKHHIWRSGHUHQWH HQHHQJHGHHOWHGDWEHWUHNNLQJKHHIWRSGHKRRIGVRP %HWDOLQJHQDDQKHWEHJLQYDQGHOHQLQJEHVWDDQXLWHHQ JURWHUGHHODDQUHQWHHQXLWHHQNOHLQHUGHHODDQGH KRRIGVRPGDQEHWDOLQJHQDDQKHWHLQGYDQHHQOHQLQJ

BETALING HOOFDSOM

RENTE

TIJD

68



*

0HWGH WRHWVYDQGH+3%,,NXQWXKHWYROJHQGHEHUHNHQHQ n +HWEHGUDJGDWLQHHQUHHNVEHWDOLQJHQEHWUHNNLQJKHHIWRSGHUHQWH n +HWEHGUDJGDWLQHHQUHHNVEHWDOLQJHQEHWUHNNLQJKHHIWRSGH KRRIGVRP n +HWVDOGRYDQGHOHQLQJQDHHQEHSDDOGDDQWDOEHWDOLQJHQ

* . /2 *b

IXQFWLHJDDWHUYDQXLWGDWX]RMXLVWHHQEHWDOLQJKHEWEHUHNHQG 'H RIGDWXGHEHWUHIIHQGHDPRUWLVDWLHZDDUGHQLQ,<539)9307HQ3 <5KHEWRSJHVODJHQ -DDUOLMNVHQRPLQDOHUHQWHYRHW %HJLQVDOGR (LQGVDOGR %HWDOLQJVEHGUDJDIJHURQGRSKHWGLVSOD\IRUPDDW $DQWDOEHWDOLQJHQSHUMDDU 'HJHWDOOHQGLHYRRUGHUHQWHGHKRRIGVRPHQKHWVDOGRZRUGHQJHWRRQG ]LMQDIJHURQGQDDUGHKXLGLJHLQVWHOOLQJYDQGHGLVSOD\

*

Het amortiseren. 8DPRUWLVHHUWHHQHQNHOYRXGLJHEHWDOLQJGRRUKHW

QXPPHUYDQGHEHWUHIIHQGHSHULRGHLQWHYXOOHQHQRS WHGUXNNHQ 'H+3%,,WRRQWGHLQGLFDWRUPERJHYROJGGRRUGHHHUVWHHQODDWVWH EHWDOLQJHQGLH]XOOHQZRUGHQJHDPRUWLVHHUG

'UXNRS RPGHUHQWHINT WHWRQHQ'UXNQRJPDDOVRS RPGH KRRIGVRPPRIN WHWRQHQHQQDQRJPDDOVWHGUXNNHQ]LHWXKHWVDOGR BAL 'RRUWHONHQVRS WHGUXNNHQNXQWXGH]HOIGHZDDUGHQRSQLHXZ EHNLMNHQ

*

0

8DPRUWLVHHUWHHQUHHNVEHWDOLQJHQGRRUKHWHHUVWHSHULRGHQXPPHU ODDWVWH SHULRGHQXPPHULQWHYRHUHQHQYHUYROJHQVRS WHGUXNNHQ'H+3 %,,WRRQWGHLQGLFDWRUPERJHYROJGGRRUGHHHUVWHHQODDWVWH EHWDOLQJHQGLH]XOOHQZRUGHQJHDPRUWLVHHUG'UXNYHUYROJHQVWHONHQVRS RPUHQWHKRRIGVRPHQVDOGRWHEHNLMNHQ

*

RPQDDUGHYROJHQGHJURHSSHULRGHVWHJDDQ 'UXNQRJPDDOVRS 'RRUGH]HDXWRPDWLVFKHYHUKRJLQJKRHIWXQLHWVLQWHWRHWVHQYRRUGH QLHXZHEHJLQHQHLQGSHULRGH

*

$OVXWLMGHQVKHWDPRUWLVHUHQRSVODDWRSYUDDJWRIHQLJHDQGHUHEHZHUNLQJ XLWYRHUWNULMJWXGRRURS WHGUXNNHQUHQWHKRRIGVRPHQVDOGRQLHW PHHUWH]LHQ$OVXGHDPRUWLVDWLHZHHUZLOWXLWYRHUHQPHWGH]HOIGH SHULRGHVGUXNWXRS 5: “Time Value of Money”-berekeningen

69


Voorbeeld: Een reeks betalingen amortiseren. %HUHNHQGHHHUVWH

WZHHMDDUYDQKHWMDDUOLMNVHDPRUWLVDWLHVFKHPDYRRUHHQK\SRWKHHNYDQ RYHUHHQSHULRGHYDQMDDUWHJHQHHQMDDUOLMNVHUHQWHYRHWYDQ PHWPDDQGHOLMNVHEHWDOLQJHQ 6WHOGH(LQGPRGXVLQ'UXNRS

*b *U . / 2 Toetsen:

*O


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQ JHQSHUMDDULQ 6ODDWKHWDDQWDOEHWDOLQ JHQRS 6ODDWGHUHQWHSHUMDDU RS 6ODDWGHKXLGLJHZDDUGH RS 6ODDWGHWRHNRPVWLJH ZDDUGHRS %HUHNHQWGHPDDQ GHOLMNVHEHWDOLQJ

360,00 7,75 180.000,00 0,00 –1.289,54

$OVXDOZHHWKRHJURRWGHEHWDOLQJRSGHK\SRWKHHNLVNXQWXGLW LQYRHUHQHQRSVODDQ]RDOVXGHDQGHUHYLHUZDDUGHQRSVODDW$PRUWLVHHU QXKHWHHUVWHMDDU

0 *

70

12_ 1– 12 –1.579,82

–13.894,66

178.420,18


9RHUWGHEHJLQHQ HLQGSHULRGHVLQ 7RRQWGH3(5LQGLFD WRUHQUHHNV 7RRQWGH35,1LQGLFD WRUHQGHKRRIGVRPGLH LQKHWHHUVWHMDDULV EHWDDOG 7RRQWGH,17LQGLFD WRUHQGHUHQWHGLHLQ KHWHHUVWHMDDULV EHWDDOG 7RRQWGH%$/LQGLFD WRUHQKHWVDOGRYDQGH OHQLQJQDppQMDDU


+HWEHGUDJGDWDDQUHQWHHQKRRIGVRPLVEHWDDOG LVJHOLMNDDQPDDQGHOLMNVHEHWDOLQJHQï +HWRSHQVWDDQGHVDOGRLVJHOLMNDDQGHEHJLQK\SRWKHHNPLQ KHWEHGUDJGDWYRRUGHKRRIGVRPLVEHWDDOG²

*

$PRUWLVHHUKHWWZHHGHMDDU 13– 24 –1.706,69

–13.767,79

176.713,49

7RRQW3(5HQGHYRO JHQGHUHHNVSHULRGHV 7RRQW35,1HQGH KRRIGVRPGLHLQKHW WZHHGHMDDULVEHWDDOG 7RRQW,17HQGHUHQWH GLHLQKHWWZHHGHMDDULV EHWDDOG 7RRQW%$/HQKHW VDOGRYDQGHOHQLQJQD EHWDOLQJHQ

+HWEHGUDJGDWDDQUHQWHHQKRRIGVRPLVEHWDDOG LVJHOLMNDDQPDDQGHOLMNVHEHWDOLQJHQï +HWRSHQVWDDQGHVDOGRLVJHOLMNDDQGHEHJLQK\SRWKHHNPLQ KHWEHGUDJGDWYRRUGHKRRIGVRPLVEHWDDOG²² (UZRUGWLQKHWWZHHGHMDDUPHHUDDQGH KRRIGVRPEHWDDOGGDQLQKHWHHUVWHMDDU'HYROJHQGHMDUHQZRUGHQRS GH]HOIGHZLM]HEHUHNHQG


71


Voorbeeld: Een enkelvoudige betaling amortiseren. $PRUWLVHHU

GHVWHVWHHQVWHEHWDOLQJYDQHHQYLMIMDDUGXUHQGH DXWROHDVH+HWEHGUDJYDQGHOHDVHLVHQGHUHQWHYRHWLV %HWDOLQJHQJHEHXUHQPDDQGHOLMNVHQHULVJHHQXLWVWHOYDQ GHHHUVWHEHWDOLQJ 6WHOGH%HJLQPRGXVLQ'UXNRS

*b *U . / 2 Toetsen:

*O


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 6ODDWKHWDDQWDOEHWDOLQJHQRS 6ODDWGHUHQWHSHUMDDURS 6ODDWGHKXLGLJHZDDUGHRS 6ODDWGHWRHNRPVWLJHZDDUGH RS %HUHNHQWGHPDDQGHOLMNVH EHWDOLQJ

60,00 11,50 14.250,00 0,00 –310,42

$PRUWLVHHUGHVWHVWHHQVWHEHWDOLQJHQ

0 * 0 *

72

1,00 1– 1 –310,42 0,00 13.939,58 25,00 25– 25 –220,21

–90,21


9RHUWGHHHUVWHEHWDOLQJLQ 7RRQW3(5HQGHJHDPRUWL VHHUGHEHWDOLQJVSHULRGH 7RRQW35,1HQGHHHUVWH EHWDOLQJDDQGHKRRIGVRP 7RRQW,17HQGHUHQWH 7RRQW%$/HQKHWVDOGRYDQ GHOHQLQJQDppQEHWDOLQJ 9RHUWGHWHDPRUWLVHUHQEHWDO LQJLQ 7RRQW3(5HQGHJHDPRUWL VHHUGHEHWDOLQJVSHULRGH 7RRQW35,1HQGHKRRIGVRP GLHELMGHVWHEHWDOLQJLV EHWDDOG 7RRQW,17HQGHUHQWHGLH RYHUGHVWHEHWDOLQJLV EHWDDOG


0 *

9.193,28 54,00 54– 54 –290,37

–20,05

1.801,57

7RRQW%$/HQKHWVDOGRYDQ GHOHQLQJQDGHVWHEHWDOLQJ 9RHUWGHWHDPRUWLVHUHQEHWDO LQJLQ 7RRQW3(5HQGHJHDPRUWL VHHUGHEHWDOLQJVSHULRGH 7RRQW35,1HQGHKRRIGVRP GLHELMGHVWHEHWDOLQJLV EHWDDOG 7RRQW,17HQGHUHQWHGLH RYHUGHVWHEHWDOLQJLV EHWDDOG 7RRQW%$/HQKHWVDOGRYDQ GHOHQLQJQDGHVWHEHWDOLQJ

Rentevoetconversies

* *Z *b

%LMGHFRQYHUVLHYDQGHUHQWHYRHWZRUGHQGULHWRHWVHQ JHEUXLNW HQ 'H]HFRQYHUWHUHQ QRPLQDOHUHQWHQDDUMDDUOLMNVHHIIHFWLHYHUHQWHHQWHUXJ 1RPLQDOHHQHIIHFWLHYHUHQWHZRUGHQRSSDJLQD EHVFKUHYHQ $OVXZHHWKRHKRRJHHQMDDUOLMNVHQRPLQDOHUHQWHLVHQX GHGDDUPHHRYHUHHQNRPHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYRHWZLOW EHUHNHQHQGRHWXKHWYROJHQGH 9RHUGHQRPLQDOHUHQWHLQHQGUXNRS 9RHUKHWDDQWDOSHULRGHVLQZDDURYHUVDPHQJHVWHOGPRHWZRUGHQHQ GUXNRS %HUHNHQGHHIIHFWLHYHUHQWHYRHWGRRURS WHGUXNNHQ

*b

* *Z *Z *

+HWEHUHNHQHQYDQHHQQRPLQDOHUHQWHGLHRYHUHHQNRPWPHWHHQEHNHQGH HIIHFWLHYHUHQWH 9RHUGHHIIHFWLHYHUHQWHLQHQGUXNRS 9RHUKHWDDQWDOSHULRGHVLQZDDURYHUPRHWZRUGHQVDPHQJHVWHOGHQ GUXNRS %HUHNHQGHQRPLQDOHUHQWHYRHWGRRURS WHGUXNNHQ

*b


73


* .

%LMGH790WRHSDVVLQJJHEUXLNHQ

HQ

KHW]HOIGHUHJLVWHU

5HQWHFRQYHUVLHVZRUGHQKRRIG]DNHOLMNELMWZHHVRRUWHQSUREOHPHQ JHEUXLNW n 9RRUKHWYHUJHOLMNHQYDQLQYHVWHULQJHQPHWYHUVFKLOOHQGHSHULRGHV ZDDURYHUGHUHQWHZRUGWVDPHQJHVWHOG n 9RRUKHWRSORVVHQYDQ790SUREOHPHQZDDUELMGHEHWDOLQJVSHULRGH HQGHUHQWHSHULRGHYHUVFKLOOHQ

Investeringen met verschillende periodes van samenstelling Voorbeeld: Investeringen vergelijken. 8RYHUZHHJWHHQ

VSDDUUHNHQLQJWHRSHQHQHQXNXQWNLH]HQXLWGULHEDQNHQ:HONHEDQN ELHGWGHEHVWHUHQWHYRRUZDDUGHQ" (HUVWHEDQN 7ZHHGHEDQN 'HUGHEDQN

MDDUOLMNVHUHQWHYRHWSHUNZDUWDDOVDPHQJHVW HOG MDDUOLMNVHUHQWHYRHWPDDQGHOLMNVVDPHQJHVWHOG MDDUOLMNVHUHQWHYRHWNHHUSHUMDDU VDPHQJHVWHOG

Eerste bank

* *b *Z Toetsen:

* *b *Z

Display:

Beschrijving:

6,70

6ODDWGHQRPLQDOHUHQWHRS 'HUHQWHZRUGWYLHUPDDOSHU MDDUVDPHQJHVWHOG %HUHNHQWGHMDDUOLMNVHHIIHF WLHYHUHQWHYRHW

4,00 6,87

Tweede bank

74

6,65 12,00 6,86


6ODDWGHQRPLQDOHUHQWHRS 6ODDWGHPDDQGHOLMNVHSHULRGHV RSZDDULQZRUGWVDPHQJHVWHOG %HUHNHQWGHMDDUOLMNVHHIIHFWLHYH UHQWHYRHW


* *b *Z

Derde bank

6,63 360,00 6,85

6ODDWGHQRPLQDOHUHQWHRS 6ODDWGHSHULRGHVRSZDDULQ ZRUGWVDPHQJHVWHOG %HUHNHQWGHMDDUOLMNVHHIIHFWLHYH UHQWHYRHW

+HWDDQERGYDQGHHHUVWHEDQNLVLHWVEHWHURPGDWJURWHULVGDQ HQ

Samenstellings- en betalingsperiodes verschillen 'H790WRHSDVVLQJJDDWHUYDQXLWGDWGH VDPHQVWHOOLQJVSHULRGHVHQGHEHWDOLQJVSHULRGHVJHOLMN]LMQ 6RPPLJHOHQLQJVWHUPLMQHQHQGHSRVLWR·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

* *b *Z *b *


75


Voorbeeld: Maandelijkse betaling, dagelijks samenstellen. 9DQDI

YDQGDDJVWRUWXPDDQGHOLMNVRSHHQUHNHQLQJZDDURYHUUHQWH ZRUGWEHWDDOGGLHGDJHOLMNVZRUGWVDPHQJHVWHOGGDJHQSHUMDDU :DW LVKHWVDOGRQD]HYHQMDDU"

Punt 1. %HUHNHQGHRYHUHHQNRPVWLJHUHQWHELMPDDQGHOLMNVH VDPHQVWHOOLQJ

* *b *Z *b * Toetsen:

Display:

Beschrijving:

5,00

6ODDWKHWSHUFHQWDJH YDQGHQRPLQDOHUHQWH RS 6ODDWKHWDDQWDO SHULRGHVRSZDDULQGH EDQNVDPHQVWHOW %HUHNHQWGHMDDUOLMNVH HIIHFWLHYHUHQWHYRHW 6ODDWGHPDDQGHOLMNVH SHULRGHVRS %HUHNHQWKHW RYHUHHQNRPVWLJH QRPLQDOHSHUFHQWDJH ZDQQHHUPDDQGHOLMNV ZRUGWVDPHQJHVWHOG

365,00

5,13 12,00 5,01

$DQJH]LHQ120HQ,<5KHW]HOIGHUHJLVWHUJHEUXLNHQNXQWXGH]H ZDDUGHGLUHFWLQGHUHVWYDQKHWYUDDJVWXNJHEUXLNHQ Punt 2. 'HWRHNRPVWLJHZDDUGHEHUHNHQHQ

(2 *U /


76

*O


0,00 –25,00 84,00 2.519,61


6ODDWGHKXLGLJHZDDUGH RS 6ODDWGHEHWDOLQJRS 6ODDWKHWDDQWDO EHWDOLQJHQSHUMDDURS %HUHNHQWKHWVDOGRQD MDDU


6 Cashflowberekeningen Het gebruiken van de cashflowfunctie 'HFDVKIORZIXQFWLHZRUGWJHEUXLNWELMKHWRSORVVHQYDQ YUDDJVWXNNHQZDDUELMFDVKIORZVPHWUHJHOPDWLJH WXVVHQSR]HQYRRUNRPHQPDDUYHUVFKLOOHQGYDQJURRWWH ]LMQ8NXQWRRNFDVKIORZEHUHNHQLQJHQXLWYRHUHQRP YUDDJVWXNNHQPHWUHJHOPDWLJHHYHQJURWHSHULRGLHNH FDVKIORZVRSWHORVVHQPDDUGH]HVLWXDWLHVNXQQHQ HIILFLsQWHUZRUGHQRSJHORVWPHW790 ,QKHWDOJHPHHQZRUGHQGHYROJHQGHSXQWHQXLWJHYRHUGELM FDVKIORZEHUHNHQLQJHQRSGH+3%,, %HNLMNXZFDVKIORZVRSSDSLHU(HQFDVKIORZGLDJUDPNDQKHHO KDQGLJ]LMQ :LVGHUHJLVWHUV 9RHUKHWDDQWDOSHULRGHVSHUMDDULQ 9RHUGHLQLWLsOHLQYHVWHULQJHQLQ 9RHUKHWEHGUDJYDQGHYROJHQGHFDVKIORZLQ $OVKHWEHGUDJGDWXLQSXQWKHEWLQJHYRHUGPHHUGDQHHQVQD HONDDUYRRUNRPWYRHUGDQKHWDDQWDONHUHQLQGDWGLWEHGUDJ YRRUNRPW +HUKDDOSXQWHQYRRULHGHUHFDVKIORZHQJURHS 8EHUHNHQWGHQHWWRKXLGLJHZDDUGHGRRUGHMDDUOLMNVHUHQWHYRHWRS WHYRHUHQHQRS WHGUXNNHQYHUYROJHQVGUXNWXRS $OVX KHWMDDUOLMNVHLQWHUQHUHQGHPHQWZLOWEHUHNHQHQGUXNWXRS

.

*N*9

6: Cashflowberekeningen

77


Voorbeeld: Een investering op korte termijn. ,QKHWYROJHQGH

FDVKIORZGLDJUDP]LHWXHHQLQYHVWHULQJLQDDQGHOHQRYHUGULHPDDQGHQ DIJHEHHOG$DQKHWEHJLQYDQLHGHUHPDDQGZHUGHQDDQNRSHQJHGDDQHQ GHDDQGHOHQZHUGHQDDQKHWHLQGYDQGHPDDQGYHUNRFKW%HUHNHQKHW MDDUOLMNVHLQWHUQHUHQGHPHQWHQKHWPDDQGHOLMNVHUHQGHPHQW

XXX

11.765,29 Ontvangen flows zijn positief.

1

2

3

-2.000,00 -4.000,00

Betaalde flows zijn negatief.

-5.000,00

*& *b (, Toetsen:

(, (, , *9 d 78


Display:

Beschrijving:

0,00

:LVWDOOHUHJLVWHUV 6ODDWSHULRGHVSHUMDDURS 9RHUWGHHHUVWHFDVKIORZLQ 7RRQWKHWQXPPHUYDQGH FDVKIORZJURHSWHUZLMOX LQJHGUXNWKRXGW 9RHUWGHYROJHQGHFDVKIORZLQ 9RHUWGHYROJHQGHFDVKIORZLQ 9RHUWGHODDWVWHFDVKIORZLQ %HUHNHQWGHMDDUOLMNVHQRPLQDOH RSEUHQJVW 0DDQGHOLMNVHRSEUHQJVW

12,00 –5.000.00

–2.000.00 –4.000,00 11.765,29 38,98 3,25

,


NPV en IRR/YR: Het verdisconteren van cashflows ,QKRRIGVWXNVWDDWDDQJHJHYHQKRHFDVKIORZGLDJUDPPHQJHEUXLNW NXQQHQZRUGHQRPILQDQFLs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sOHEHJULSSHQZRUGWGXLGHOLMNQDKHW XLWZHUNHQYDQHHQSDDUYRRUEHHOGHQ,QGHYROJHQGHWZHHSDUDJUDIHQ NRPWKHWJURHSHUHQHQLQYRHUHQYDQFDVKIORZVDDQGHRUGH'DDUQD YROJHQHQNHOHYRRUEHHOGHQYDQ139HQ,55<5EHUHNHQLQJHQ

Cashflows groeperen (HQUHHNVYDQFDVKIORZVZRUGWJHJURHSHHUGLQHHQHHUVWHFDVKIORZ&) HQ GDDURSYROJHQGHFDVKIORZJURHSHQPD[LPDDOFDVKIORZV &)NRPWDDQ KHWEHJLQYDQGHHHUVWHSHULRGH(HQFDVKIORZJURHSEHVWDDWXLWKHWEHGUDJ ZDDUXLWGHFDVKIORZEHVWDDWHQKHWDDQWDOKHUKDOLQJHQ ,QKHWYROJHQGHFDVKIORZGLDJUDPLVGHHHUVWHFDVKIORZELMYRRUEHHOG ²'HYROJHQGHJURHSFDVKIORZVEHVWDDWXLW]HVFDVKIORZVYDQHON QXOJHYROJGGRRUHHQJURHSYDQGULHFDVKIORZVYDQHON'HODDWVWH JURHSEHVWDDWXLWppQFDVKIORZYDQ


79


CF

CF

CF

1

CFO

1

=

0,

2

=

N

1

=

3

2

=

1 . 0 0 0,

3

N

=

2

1 0 . 0 0 0,

=

N

3

=

1

3

6

4

5

6

7

8

9

10

-11.000

:DQQHHUXHHQVHULHFDVKIORZVLQYRHUWLVKHWYDQEHODQJGDWLHGHUH FDVKIORZLQKHWFDVKIORZGLDJUDPZRUGWYDVWJHOHJG]HOIVELMSHULRGHVPHW HHQFDVKIORZYDQQXO

Cashflows invoeren ,QGH+3%,,NXQWXHHQHHUVWHFDVKIORZRSVODDQHQGDDUQDQRJ H[WUDFDVKIORZJURHSHQ(ONHFDVKIORZJURHSNDQWRWFDVKIORZV EHYDWWHQ8YRHUWFDVKIORZVDOVYROJWLQ 'UXNRS RPGHUHJLVWHUVWHZLVVHQ 9RHUKHWDDQWDOSHULRGHVSHUMDDULQHQGUXNRS 9RHUKHWEHGUDJYDQGHHHUVWHLQYHVWHULQJLQHQGUXNYHUYROJHQVRS 'H´MµJHHIWKHWQXPPHUYDQGHFDVKIORZDDQWRWHQPHW 9RHUKHWEHGUDJYDQGHYROJHQGHFDVKIORZLQHQGUXNRS $OVKHWEHGUDJGDWLQSXQWZHUGLQJHYRHUGPHHUGDQHHQVQDHONDDU YRRUNRPWYRHUWXLQKRHYDDNGLWJHEHXUWHQGUXNWXRS +HUKDDOSXQWHQYRRULHGHUH HQ WRWGDWDOOHFDVKIORZV ]LMQLQJHYRHUG

*&

*b

,

, *C

80


, *C


Voorbeeld. 9RHUGHFDVKIORZVYDQKHWYRRUJDDQGHGLDJUDPLQHQ EHUHNHQGH,55<5%HUHNHQYHUYROJHQVGHHIIHFWLHYHUHQWH1HHPDDQ GDWHUSHULRGHVSHUMDDU]LMQ

*& *b (, Toetsen:

, *C , *C , *9

Display:

Beschrijving:

0,00

:LVWDOOHUHJLVWHUV 6WHOW RSLQ 9RHUWGHHHUVWHFDVKIORZLQ 7RRQWKHWQXPPHUYDQGH FDVKIORZJURHSWHUZLMOX LQJHGUXNWKRXGW 9RHUWKHWEHGUDJYDQGHHHUVWH FDVKIORZJURHSLQ 9RHUWKHWDDQWDONHUHQLQGDWGLW ZRUGWKHUKDDOG 9RHUWKHWEHGUDJYDQGHWZHHGH FDVKIORZJURHSLQ 9RHUWKHWDDQWDONHUHQLQGDWGLW ZRUGWKHUKDDOG 9RHUWGHODDWVWHFDVKIORZLQ %HUHNHQWGHMDDUOLMNVHQRPLQDOH RSEUHQJVW

12,00 –11.000,00

0,00 6,00 1.000,00 3,00 10.000,00 21,22

b

,

Cashflows bekijken en vervangen 8NXQWHHQOLMVWPHWFDVKIORZVEHNLMNHQGRRURSGHYROJHQGHWRHWVHQWH GUXNNHQ n WRW RPFDVKIORZVWRWWHEHNLMNHQRI n WRW RPFDVKIORZVWRWZHHUWHJHYHQ n RPGHYROJHQGHFDVKIORZWH]LHQ n RPGHYRULJHFDVKIORZWH]LHQRI n RPGHKXLGLJHFDVKIORZWH]LHQ

, , , , ,,


81


2PKHWEHGUDJYDQHHQFDVKIORZWHYHUYDQJHQGUXNWXRS n WRW RPKHWQLHXZHEHGUDJRSWHVODDQLQFDVKIORZV WRWRI n WRW RPKHWQLHXZHEHGUDJRSWHVODDQLQFDVKIORZV WRW n RPKHWEHGUDJRSWHVODDQLQGHYROJHQGHFDVKIORZ n RPKHWEHGUDJRSWHVODDQLQGHYRULJHFDVKIORZ n RPKHWEHGUDJRSWHVODDQLQGHKXLGLJHFDVKIORZ

!, !, !, !, !,,

$OVXKHWDDQWDONHUHQGDWHHQFDVKIORZYRRUNRPWZLOWDDQSDVVHQ GH FDVKIORZZDDUYRRUXGLWZLOWGRHQ9RHUYHUYROJHQVKHWDDQWDONHUHQLQ GDWGH]HPRHWYRRUNRPHQHQGUXNRS

*C

*&

$DQJH]LHQFDVKIORZVQLHWYHUZLMGHUGRIWXVVHQJHYRHJGNXQQHQZRUGHQ RPRSQLHXZWHEHJLQQHQ JHEUXLNWX

De netto huidige waarde berekenen 'HQHWWRKXLGLJHZDDUGHIXQFWLH139 ZRUGWJHEUXLNWRPDOOH FDVKIORZVWHYHUGLVFRQWHUHQGLHYRRUGHWLMGOLMQVWDDQPHWEHKXOSYDQHHQ MDDUOLMNVHQRPLQDOHUHQWHYRHWGLHXLQYRHUW +LHURQGHU]LHWXKRHX139EHUHNHQW 'UXNRS VODKHWDDQWDOSHULRGHVSHUMDDULQ3<5RS 9RHUGHFDVKIORZVLQPHW HQ 6ODGHMDDUOLMNVHQRPLQDOHUHQWHYRHWLQ,<5RSHQGUXNRS

*&

, C

*N

Voorbeeld: Een verdisconteerd contract, ongelijke cashflows. 8

NXQWHHQFRQWUDFWNRSHQPHWGHYROJHQGHFDVKIORZV

82

Eind van de maand

Bedrag



:DWPRHWXYRRUKHWFRQWUDFWEHWDOHQDOVXHHQMDDUOLMNVUHQGHPHQWYDQ RSXZLQYHVWHULQJZLOWKDOHQ"

I/YR = 15% 5.000 4

*& *b , Toetsen:

, *C , , *C , *C , *C , , *C ,

10.000 5.000 9 10

7.500

15

25

Display:

Beschrijving:

0,00

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

12,00 0,00

0,00 3,00 5.000,00 0,00 4,00 5.000,00 2,00 0,00 4,00 7.500,00 0,00 9,00 10.000,00

,


83


*C,

,

'HFDVKIORZVGLHXZWRHNRPVWLJHLQYHVWHULQJEHVFKULMYHQVWDDQQXLQGH FDOFXODWRU8NXQWRS GUXNNHQHQGDDUQDRS HQELM KHUKDOLQJRS RPGHFDVKIORZVHQKHWDDQWDONHUHQGDWGH]H YRRUNRPHQWHEHNLMNHQ 1DGDWXGHFDVKIORZVKHEWLQJHYRHUGVODDWXGHUHQWHYRHWRSHQEHUHNHQW XGHQHWWRKXLGLJHZDDUGH

. *N

Toetsen:

Display:

Beschrijving:

15,00

6ODDWGHJHZHQVWH MDDUOLMNVHUHQWHYRHWRS %HUHNHQWGHQHWWR KXLGLJHZDDUGHYDQ LHGHUHFDVKIORZGLHLV RSJHVODJHQ=LHKHW YRRUEHHOGRYHU DIURQGHQRS SDJLQD

27.199,92

8LWKHWUHVXOWDDWEOLMNWGDWDOVXHHQUHQGHPHQWYDQSHUMDDUZLOW KHEEHQXYRRUKHWFRQWUDFWPRHWEHWDOHQ8]LHWGDWGLWHHQ SRVLWLHIEHGUDJLV'HQHWWRKXLGLJHZDDUGHEHVWDDWXLWGHELMHONDDU RSJHWHOGHZDDUGHQYDQHHQVHULHYDQFDVKIORZVZDQQHHU]LMQDDUKHWEHJLQ YDQGHWLMGOLMQZRUGHQYHUGLVFRQWHHUG

NPV = 27.199,92 7.330,34 6.224,95

1% = 15% per jaar

4.415,91

10.000,00 7.500,00

4.471,10 4.757,62

84

5.000,00 1

3

5

7 9


11 13 15 17 19 21 23 25


Het interne rendement berekenen

*& *9

'UXNRS VODKHWDDQWDOSHULRGHVSHUMDDULQ3<5RS 9RHUGHFDVKIORZVLQPHW HQ 'UXNRS

, C

$OVX,55<5EHUHNHQWNULMJWXGHMDDUOLMNVHQRPLQDOHUHQWHGLHXHHQ 139YDQQXOJHHIW ,QKHWYROJHQGHYRRUEHHOGZRUGHQGH]HOIGHFDVKIORZVJHEUXLNWDOVELMKHW YRULJHYRRUEHHOG (ULVPHHUGDQppQ,55<5PRJHOLMN$OVXGHPHOGLQJno SoLution NULMJWUDDGSOHHJGDQ$DQKDQJVHO%SDJLQD Voorbeeld. $OVGHYHUNRSHUYDQKHWFRQWUDFWXLWKHWYRULJHYRRUEHHOG YHUODQJWHQXDFFHSWHHUWGLHSULMVZDWLVGDQXZUHQGHPHQW"'LW LVHHQ,55<5EHUHNHQLQJZDDUYRRUHHQNOHLQHYHUDQGHULQJDDQGHRSGLW RJHQEOLNRSJHVODJHQFDVKIORZVQRGLJLV 10.000

5.000

1

3

5

7.500

5.000

7

9

11

13

15

17

19

21

23

25

IRR/YR = ?

-28.000

(*! , *9 Toetsen:

Display:

Beschrijving:

–28.000,00

:LM]LJWGHHHUVWHFDVKIORZ

12,49

%HUHNHQWGHMDDUOLMNVHQRPLQDOH RSEUHQJVW

8YLQGWQRJPHHUYRRUEHHOGHQZDDULQ139HQ,55<5YRRUNRPHQLQ KRRIGVWXN´([WUDYRRUEHHOGHQµ


85


Automatische opslag van IRR/YR en NPV

$OVX,55<5EHUHNHQWZRUGWKHWUHVXOWDDWRRNLQ,<5RSJHVODJHQ%LM KHWYRULJHYRRUEHHOGGUXNWXRS.RPGHMDDUOLMNVHRSEUHQJVW WHWRQHQ

$OVXGH139EHUHNHQWZRUGWKHWUHVXOWDDWLQ39RSJHVODJHQ$OVXGDW UHVXOWDDWZLOWRSYUDJHQGUXNWXRS $OVXGH790ZDDUGHQXLWKHW ODDWVWHYRRUEHHOGZDDULQPHW139ZHUGJHZHUNWSDJLQD QLHWKHEW YHUDQGHUGLVKHWUHVXOWDDWDOVXRS GUXNW

86



7 Statistische berekeningen

A *@

'HWRHWVHQ HQ ZRUGHQJHEUXLNWRPJHJHYHQV YRRUVWDWLVWLHNHQPHWppQRIWZHHYDULDEHOHQLQWHYRHUHQRI WHYHUZLMGHUHQ6RPPDWLHJHJHYHQVZRUGHQRSJHVODJHQLQ KHWJHKHXJHQ'HODEHOVGLHERYHQGH WRW WRHWVHQ VWDDQJHYHQDDQZHONVWDWLVWLVFKJHJHYHQLQKHWEHWUHIIHQGH UHJLVWHULVRSJHVODJHQ1DGDWXGHJHJHYHQVKHEWLQJHYRHUG NXQWXGHVWDWLVWLVFKHIXQFWLHVJHEUXLNHQRPKHWYROJHQGH

WHEHUHNHQHQ n *HPLGGHOGHHQVWDQGDDUGGHYLDWLH n /LQHDLUHUHJUHVVLH n /LQHDLUHEHQDGHULQJHQYHUZDFKWLQJHQ n *HZRJHQJHPLGGHOGH n 6RPPDWLHVWDWLVWLHNHQQΣ[Σ[Σ\Σ\HQΣ[\

Statistische gegevens wissen :LVGHVWDWLVWLVFKHUHJLVWHUVYRRUGDWXQLHXZHJHJHYHQV LQYRHUW$OVXGHUHJLVWHUVQLHWZLVWZRUGHQGHJHJHYHQV GLHRSGLWRJHQEOLN]LMQRSJHVODJHQDXWRPDWLVFK RSJHQRPHQLQGHVRPPDWLHEHUHNHQLQJHQ8ZLVWGH VWDWLVWLVFKHUHJLVWHUVGRRURS WHGUXNNHQ'HGLVSOD\ ZRUGWGDQHYHQHHQVJHZLVW

*j

7: Statistische berekeningen

87


Statistische gegevens invoeren 8NXQWHHQRQEHJUHQVGDDQWDOZDDUGHQLQGHVWDWLVWLVFKHUHJLVWHUV YHU]DPHOHQ

Statistieken met één variabele 8JDDWDOVYROJWWHZHUNELMKHWLQYRHUHQYDQGH[JHJHYHQVELMVWDWLVWLHNHQ PHWppQYDULDEHOH :LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS WHGUXNNHQ 9RHUGHHHUVWHZDDUGHLQHQGUXNRS 'H+3%,,WRRQWQKHW DDQWDOYHU]DPHOGHJHJHYHQV *DYHUGHUPHWKHWWRHYRHJHQYDQZDDUGHQGRRUGHJHWDOOHQLQWH YRHUHQHQRS WHGUXNNHQ'HQZDDUGHZRUGWELMLHGHUHLQYRHU YHUKRRJG

*j A

A

Statistieken met twee variabelen en gewogen gemiddelde 8YRHUWDOVYROJW[\SDUHQYDQVWDWLVWLVFKHJHJHYHQVLQ :LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS WHGUXNNHQ 9RHUGHHHUVWH[ZDDUGHLQHQGUXNRS 'H+3%,,JHHIWGH[ ZDDUGHZHHU 9RHUGHRYHUHHQNRPVWLJH\ZDDUGHLQHQGUXNRS 'H+3%,, JHHIWQKHWDDQWDOYHU]DPHOGHSDUHQZHHU *DYHUGHUPHWKHWLQYRHUHQYDQ[\SDUHQ'HQZDDUGHZRUGWELM LHGHUHLQYRHUYHUKRRJG

*j 0

A

8YRHUWJHJHYHQVYRRUKHWEHUHNHQHQYDQKHWJHZRJHQJHPLGGHOGHLQ GRRULHGHUHZDDUGHDOV[LQWHYRHUHQHQGHRYHUHHQNRPVWLJH ZHJLQJVFRsIILFLsQWDOV\

88

Als door de statistische gegevens de waarde in een register groter wordt dan ±9,99999999999 × 10499, toont de HP 10BII een tijdelijke overflow melding (OFLO).



Statistische gegevens verbeteren

*@

2QMXLVWLQJHYRHUGHJHJHYHQVNXQQHQYHUZLMGHUGZRUGHQPHW $OV ppQYDQGHZDDUGHQYDQHHQ[\SDDURQMXLVWLVPRHWXEHLGHZDDUGHQ YHUZLMGHUHQHQRSQLHXZLQYRHUHQ

Verbeteren van gegevens bestaande uit één variabele +HWYHUZLMGHUHQHQRSQLHXZLQYRHUHQYDQVWDWLVWLVFKHJHJHYHQVJDDWDOV YROJW 7RHWVGH[ZDDUGHLQGLHYHUZLMGHUGPRHWZRUGHQ 'UXNRS RPGHZDDUGHWHYHUZLMGHUHQ'HQZDDUGHZRUGW PHWppQYHUPLQGHUG 9RHUGHMXLVWHZDDUGHLQPHW

*@

A

Verbeteren van gegevens bestaande uit twee variabelen +HWYHUZLMGHUHQHQRSQLHXZLQYRHUHQYDQ[\SDUHQVWDWLVWLVFKHJHJHYHQV JDDWDOVYROJW 9RHUGH[ZDDUGHLQGUXNRS HQYRHUYHUYROJHQVGH\ZDDUGHLQ 'UXNRS RPGHZDDUGHQWHYHUZLMGHUHQ'HQZDDUGHZRUGW PHWppQYHUPLQGHUG 9RHUKHWMXLVWH[\SDDULQPHW HQ

*@

0

0 A


89


Samenvatting van statistische berekeningen 6RPPLJHIXQFWLHVOHYHUHQWZHHZDDUGHQRS'HSTAT LQGLFDWRUJHHIWDDQ GDWWZHHZDDUGHQ]LMQEHUHNHQG'UXNRS RPGHYHUERUJHQ ZDDUGHWH]LHQ

*i

Toetsen

*$ *E

*: *M *3 [ZDDUGH *4 *4 \ZDDUGH

Beschrijving

5HNHQNXQGLJ JHPLGGHOGHYDQGH[ ZDDUGHQ

*i naar display *HPLGGHOGHYDQGH\ ZDDUGHQDOVX\ZDDUGHQ KHEWLQJHYRHUG

*HPLGGHOGHYDQGH[ ZDDUGHQJHZRJHQ YROJHQVGH\ZDDUGHQ 6WHHNSURHIVWDQGDDUGGHYL 6WHHNSURHIVWDQGDDUGGHYL DWLHYDQGH[ZDDUGHQ DWLHYDQGH\ZDDUGHQDOV X\ZDDUGHQKHEW LQJHYRHUG 3RSXODWLHVWDQGDDUGGHYLD 3RSXODWLHVWDQGDDUGGHYLD WLHYDQGH[ZDDUGHQ WLHYDQGH\ZDDUGHQDOV X\ZDDUGHQKHEW LQJHYRHUG %HQDGHULQJYDQ[ELMHHQ &RUUHODWLHFRsIILFLsQW JHJHYHQZDDUGHYDQ\ %HQDGHULQJYDQ\ELMHHQ 5LFKWLQJVFRsIILFLsQWP JHJHYHQZDDUGHYDQ[ YDQGHEHUHNHQGHOLMQ VQLMSXQWPHWGH\DVE YDQ 5LFKWLQJVFRsIILFLsQWP GHEHUHNHQGHOLMQ YDQGHEHUHNHQGHOLMQ

'HVWHHNSURHIVWDQGDDUGGHYLDWLHJDDWHUYDQXLWGDWGHJHJHYHQVHHQVWHHNSURHI]LMQYDQHHQJURWHUHPHHU YROOHçGLJHYHU]DPHOLQJYDQJHJHYHQV%LMGHSRSXODWLHVWDQGDDUGGHYLDWLHZRUGWHU YDQXLWJHJDDQGDWGHJHJHYHQV JHOLMN]LMQDDQGHJHKHOHSRSXODWLH

'HFRUUHODWLHFRsIILFLsQWLVHHQJHWDOGDWWXVVHQ²HQOLJWHQGDWDDQJHHIWKRHQDXZNHXULJGHEHUHNHQGHOLMQ GHJHJHYHQVEHQDGHUW(HQZDDUGHYDQJHHIWHHQYRONRPHQSRVLWLHYHFRUUHODWLHHQ²JHHIWHHQYRONRPHQ QHJDWLHYHFRUUHODWLHDDQ(HQZDDUGHGLHLQGHEXXUWYDQQXOOLJWJHHIWDDQGDWGHOLMQJHHQJRHGHEHQDGHULQJLV

90



)+ ); )= )\ )g )f

Toetsen

Beschrijving

$DQWDOLQJHYRHUGHJHJHYHQVSXQWHQ 6RPYDQGH[ZDDUGHQ 6RPYDQGH\ZDDUGHQ 6RPYDQGHNZDGUDWHQYDQGH[ZDDUGHQ 6RPYDQGHNZDGUDWHQYDQGH\ZDDUGHQ 6RPYDQGHSURGXFWHQYDQGH[DQG\ ZDDUGHQ

Gemiddelde, standaarddeviatie en sommatiestatistieken 8NXQWKHWJHPLGGHOGH [ GH VWHHNSURHIVWDQGDDUGGHYLDWLH6[ HQ SRSXODWLHVWDQGDDUGGHYLDWLHσ[ HQVRPPDWLHVWDWLVWLHNHQ QΣ[HQΣ[YDQ[JHJHYHQVEHUHNHQHQ9RRUGH[\ JHJHYHQVNXQWXRRNKHWJHPLGGHOGHGH VWHHNSURHIVWDQGDDUGGHYLDWLHHQGH SRSXODWLHVWDQGDDUGGHYLDWLHYDQ\JHJHYHQVHQGH VRPPDWLHVWDWLVWLHNHQΣ\Σ\HQΣ[\EHUHNHQHQ Voorbeeld 1. 'HNDSLWHLQYDQHHQMDFKWZLOEHSDOHQKRHYHHOWLMGKHWNRVW

RPHHQ]HLOWHYHUZLVVHOHQ=LMNLHVWKLHUYRRU]HVZLOOHNHXULJHOHGHQYDQ KDDUEHPDQQLQJREVHUYHHUWKHQELMKHWZLVVHOHQYDQKHW]HLOHQVFKULMIW KHWEHQRGLJGHDDQWDOPLQXWHQRS%HUHNHQKHW JHPLGGHOGHHQGHVWDQGDDUGGHYLDWLHYDQGHWLMGHQ%HUHNHQRRNGHZRUWHO XLWKHWJHPLGGHOGHYDQGHNZDGUDWHQPHWGHIRUPXOH ∑ x 2 ⁄ n Toetsen:

*j A A A A A

Display:

Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV 9RHUWGHHHUVWHWLMGLQ 9RHUWGHWZHHGHWLMGLQ 9RHUWGHGHUGHWLMGLQ 9RHUWGHYLHUGHWLMGLQ 9RHUWGHYLMIGHWLMGLQ

1,00 2,00 3,00 4,00 5,00


91


A *$ *: )\ d)+ *T

6,00 3,50 0,85 77,13 6,00 3,59

9RHUWGH]HVGHWLMGLQ %HUHNHQWKHWJHPLGGHOGH %HUHNHQWGHVWHHNSURHI VWDQGDDUGGHYLDWLH *HHIWΣ[ZHHU *HHIWQZHHU %HUHNHQWKHWNZDGUDWLVFK JHPLGGHOGH

*:

'HVWDQGDDUGGHYLDWLHVGLH]LMQEHUHNHQGPHW HQ ]LMQGHVWHHNSURHIVWDQGDDUGGHYLDWLHV+LHUELM ZRUGWDDQJHQRPHQGDWKHWRPHHQJURWHUHYROOHGLJH YHU]DPHOLQJYDQJHJHYHQVJDDW

*: *i

$OVGHJHJHYHQVGHJHKHOHSRSXODWLHYHUWHJHQZRRUGLJHQ NDQGHZHUNHOLMNHSRSXODWLHVWDQGDDUGGHYLDWLHZRUGHQ HQ WHGUXNNHQ EHUHNHQGGRRURS

*M *M*i

Voorbeeld 2. 'HFRDFKKHHIWYLHUQLHXZHVSHOHUVLQKHWWHDPGLH

HQFPODQJ]LMQHQHQNJZHJHQ%HUHNHQKHW JHPLGGHOGHHQGHSRSXODWLHVWDQGDDUGGHYLDWLHYDQKXQOHQJWHHQJHZLFKW HQVRPPHHUYHUYROJHQVGH\ZDDUGHQ Toetsen:

*j 0A 0A 0A 0A *$ *i

92

Display:

Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV 9RHUWGHOHQJWHHQKHW JHZLFKWYDQVSHOHULQ 9RHUWGHOHQJWHHQKHW JHZLFKWYDQVSHOHULQ 9RHUWGHOHQJWHHQKHW JHZLFKWYDQVSHOHULQ 9RHUWGHOHQJWHHQKHW JHZLFKWYDQVSHOHULQ %HUHNHQWKHWJHPLGGHOGH YDQGHOHQJWHV[ *HHIWKHWJHPLGGHOGH YDQGHJHZLFKWHQZHHU \

1,00 2,00 3,00 4,00 184,25 82,75



*M

5,80

*i

4,71

)=

331,00

%HUHNHQWGHSRSXODWLHV WDQGDDUGGHYLDWLHYDQGH OHQJWHV[ *HHIWGH SRSXODWLHVWDQGDDUGGHYLDWL HYDQGHJHZLFKWHQZHHU \ *HHIWKHWWRWDDOYDQ\ ZHHU

Lineaire regressie en benadering /LQHDLUHUHJUHVVLHLVHHQVWDWLVWLVFKHPHWKRGHYRRUKHW PDNHQYDQEHQDGHULQJHQHQYHUZDFKWLQJHQ'HPHWKRGH ZRUGWJHEUXLNWRPHHQUHFKWHOLMQWHYLQGHQGLH]RJRHG PRJHOLMNGRRUHHQYHU]DPHOLQJ[\JHJHYHQVJHWURNNHQ NDQZRUGHQ(UPRHWHQWHQPLQVWHWZHHYHUVFKLOOHQGH[\ SDUHQ]LMQ'HUHFKWHOLMQJHHIWGHUHODWLHWXVVHQGH[HQ\ YDULDEHOHQZHHU\ P[EZDDUELMPGH ULFKWLQJVFRsIILFLsQWLVHQEKHWVQLMSXQWPHWGH\DV Lineaire regressie. %HUHNHQPEHQUGHFRUUHODWLHFRsIILFLsQW DOVYROJW

*j 0

:LVGHVWDWLVWLVFKHUHJLVWHUVGRRURS WHGUXNNHQ 9RHUGHHHUVWH[ZDDUGHLQHQGUXNRS 'H+3%,,JHHIWGH[ ZDDUGHZHHU 9RHUGHRYHUHHQNRPVWLJH\ZDDUGHLQHQGUXNRS 'H+3%,, JHHIWQKHWDDQWDOYHU]DPHOGHSDUHQZHHU *DYHUGHUPHWKHWLQYRHUHQYDQ[\SDUHQ'HQZDDUGHZRUGWELM LHGHUHLQYRHUYHUKRRJG 8YLQGWEKHWVQLMSXQWPHWGH\DV GRRURS WHGUXNNHQ 9HUYROJHQVGUXNWXRS RPPGHULFKWLQJVFRsIILFLsQWYDQGH OLMQ WHNULMJHQ 8YLQGWUGHFRUUHODWLHFRsIILFLsQWGRRURS WHGUXNNHQ

A

*i

*4

*3*i


93


Lineaire benadering. 'HUHFKWHOLMQGLHGRRUOLQHDLUHUHJUHVVLHLV EHUHNHQGNDQZRUGHQJHEUXLNWRPHHQEHQDGHULQJYDQHHQ\ZDDUGHWH YLQGHQELMHHQJHJHYHQ[ZDDUGHHQRPJHNHHUG 9RHUGH[\JHJHYHQVLQYROJHQVGHLQVWUXFWLHVRSSDJLQD 9RHUGHEHNHQGH[ZDDUGHRI\ZDDUGHLQ n $OVXHHQEHQDGHULQJYDQ[ZLOWKHEEHQYRRUGHJHJHYHQ\YRHUW XGH\ZDDUGHLQHQGUXNWXYHUYROJHQVRS n $OVX\ZLOWEHQDGHUHQYRRUHHQJHJHYHQ[YRHUWXGH[ZDDUGH LQHQGUXNWXYHUYROJHQVRS

*3

*4

Voorbeeld: verwachtingen $OL·V$]DOHDVPDDNWUHFODPHRSHHQ SODDWVHOLMNUDGLRVWDWLRQ*HGXUHQGHGHDIJHORSHQ]HVZHNHQKHHIWGHEDDV ELMJHKRXGHQKRHYHHOPLQXWHQUHFODPHHUJHNRFKWZHUGHQHQKRHYHHO D]DOHD·VHUGLHZHHN]LMQYHUNRFKW Week

Minuten reclame (x-waarden)

Verkoop (y-waarden)

%HUHNHQKHWVQLMSXQWPHWGH\DVGHULFKWLQJVFRsIILFLsQWHQGH FRUUHODWLHFRsIILFLsQW

94



y 3.000,00

(verwachtingen)

2.000,00

m = 425,88

Verkoop ($)

1.000,00 b x 1

2

3

4

5

6

7

8

Minuten reclame

Toetsen:

*j 0A 0A 0A 0A 0A 0A *4 *i *3*i

Display:

Beschrijving:

0,00

:LVWVWDWLVWLVFKHUHJLVWHUV 9RHUWPLQXWHQHQYHUNRRS LQYRRUGHDFKWHUHHQYRO JHQGHZHNHQ

1,00

2,00 3,00 4,00 5,00 6,00 376,25 425,88 0,90

%HUHNHQWKHWVQLMSXQWPHW GH\DVE *HHIWGHULFKWLQJVFRsI ILFLsQWZHHU %HUHNHQWGHFRUUH ODWLHFRsIILFLsQW


95


0DDNWHHQVFKDWWLQJYDQKHWYHUNRRSFLMIHUDOVKHWEHGULMIRIPLQXWHQ UHFODPHNRRSW

*4

3.357,38

*4

3.783,25

0DDNWHHQVFKDWWLQJ YDQKHWYHUNRRSFLMIHU DOVPLQXWHQUHFODPH ZRUGHQJHNRFKW 0DDNWHHQVFKDWWLQJ YDQKHWYHUNRRSFLMIHU DOVPLQXWHQUHFODPH ZRUGHQJHNRFKW

+RHYHHOPLQXWHQUHFODPHPRHW$OL·VNRSHQRPHHQYHUNRRSFLMIHUYDQ WHEHKDOHQ"

*3

6,16

0DDNWHHQVFKDWWLQJ YDQKHWDDQWDOPLQXWHQ UHFODPHQRGLJYRRUHHQ YHUNRRSFLMIHUYDQ

Gewogen gemiddelde 2SGHYROJHQGHPDQLHUZRUGWKHWJHZRJHQJHPLGGHOGHYDQ JHJHYHQVSXQWHQEHUHNHQG[[«[QPHWELMEHKRUHQGH ZHJLQJVFRsIILFLsQWHQ\\«\Q

0 A *E

*HEUXLN HQ RP[\SDUHQLQWHYRHUHQ'H\ZDDUGHQ]LMQGH JHZLFKWHQYDQGH[ZDDUGHQ 'UXNRS Voorbeeld. %LMHHQRQGHU]RHNQDDUGHKXXUSULMVYDQHHQNDPHUIODWV EOLMNWGDWIODWVYHUKXXUGZRUGHQYRRUKXXUSHUPDDQGYRRU YRRUHQYRRU:DWLVGHJHPLGGHOGHKXXUSULMVSHU PDDQG"

96



Toetsen:

*j 0A

Display:

Beschrijving:

0,00

:LVWKHWVWDWLVWLVFKH JHKHXJHQ 9RHUWGHHHUVWHKXXUHQ KHWGDDUELMEHKRUHQGH JHZLFKWLQ 9RHUWGHWZHHGHKXXU HQKHWGDDUELM EHKRUHQGHJHZLFKWLQ 9RHUWGHGHUGHKXXUHQ KHWGDDUELMEHKRUHQGH JHZLFKWLQ 9RHUWGHYLHUGHKXXU HQKHWGDDUELM EHKRUHQGHJHZLFKWLQ %HUHNHQWKHWJHZRJHQ JHPLGGHOGH

1,00

0A

2,00

0A

3,00

0A

4,00

*E

509,44


97



8 Extra voorbeelden Economische toepassingen Het vaststellen van een verkoopprijs (HQPHWKRGHYRRUKHWYDVWVWHOOHQYDQGHYHUNRRSSULMVSHUHHQKHLGLVKHW EHSDOHQYDQGHSURGXFWLHNRVWHQSHUHHQKHLGHQGH]HWHYHUPHQLJYXOGLJHQ PHWKHWJHZHQVWHUHQGHPHQW2PWRWHHQQDXZNHXULJUHVXOWDDWWHNRPHQ PRHWXDOOHNRVWHQGLHDDQKHWSURGXFW]LMQYHUERQGHQYDVWVWHOOHQ 0HWGHYROJHQGHIRUPXOHZRUGWGHSULMVSHUHHQKHLGEHUHNHQGRSEDVLV YDQGHWRWDOHNRVWHQHQKHWUHQGHPHQW 35,-6 727$/(.267÷$$17$/((1+('(1ï571÷ Voorbeeld. +HWNRVWRPHHQKHGHQWHSURGXFHUHQ8ZLOW UHQGHPHQW:HONHSULMVPRHWXSHUHHQKHLGYUDJHQ"

d " * * d Toetsen:

Display:

Beschrijving:

40,000.00

9RHUWGHNRVWHQLQ %HUHNHQWGHNRVWHQSHU HHQKHLG %HUHNHQWGH YHUNRRSSULMVSHU HHQKHLG

20,00 24,00

8: Extra voorbeelden

99


Verwachtingen gebaseerd op historische gegevens (HQPHWKRGHYRRUKHWEHSDOHQYDQYHUNRRSYHUZDFKWLQJHQ SURGXFWLHNRVWHQRIXLWJDYHQLVKHWEHNLMNHQYDQKLVWRULVFKHWHQGHQVHQ $OVXKLVWRULVFKHJHJHYHQVKHEWNDQKLHUGRRUHHQNURPPHJHWURNNHQ ZRUGHQZDDUELMGHWLMGODQJVGH[DVORRSWHQGHKRHYHHOKHLGODQJVGH\ DV Voorbeeld. :DWLVKHWYHUZDFKWHYHUNRRSFLMIHULQMDDU]HVHQ]HYHQ JHJHYHQGHYROJHQGHYHUNRRSLQIRUPDWLH"

*j 0A 0A 0A 0A 0A *4 Toetsen:

*4

100 8: Extra voorbeelden

Jaar

Verkoop $

1 2 3 4 5

10.000 11.210 13.060 16.075 20.590

Display:

Beschrijving:

0,00

:LVWGHVWDWLVWLVFKH UHJLVWHUV 9RHUWKHWHHUVWHMDDULQ HQKHWYHUNRRSFLMIHU 9RHUWGHJHJHYHQVYDQ KHWWZHHGHMDDULQ *DDWYHUGHUPHWKHW LQYRHUHQYDQJHJHYHQV

1,00 2,00 3,00 4,00 5,00 22.000,50

24.605,00

9HUZDFKWH YHUNRRSFLMIHUYRRUMDDU ]HV 9HUZDFKWH YHUNRRSFLMIHUYRRUMDDU ]HYHQ


Kosten indien niet contant wordt betaald (HQNRSHUNULMJWNRUWLQJELMFRQWDQWHEHWDOLQJDOVGHEHWDOLQJELQQHQHHQ EHSDDOGHSHULRGHSODDWVYLQGW%LMYRRUEHHOGGHYHUPHOGLQJ´ 1(7µRSGHIDFWXXUEHWHNHQWGDWGHNRSHUSURFHQWNDQDIWUHNNHQ DOVGHEHWDOLQJELQQHQGDJHQSODDWVYLQGW$OVGHEHWDOLQJQLHWELQQHQ GDJHQSODDWVYLQGWPRHWKHWJHKHOHEHGUDJYRRUGHVWHGDJEHWDDOG ]LMQ 0HWGHIRUPXOHKLHURQGHUNXQWXEHUHNHQHQZDWKHWXNRVWDOVXJHHQ JHEUXLNPDDNWYDQNRUWLQJELMFRQWDQWHEHWDOLQJ'HNRVWHQZRUGHQ EHUHNHQGDOVHHQMDDUOLMNVHUHQWHGLHYRRUKHWXLWVWHOOHQYDQGHEHWDOLQJLQ UHNHQLQJZRUGWJHEUDFKW .257 × × .267 = -------------------------------------------------------------------------------------------------------------------------( ( – .257 ) × (727'*1 – .257'*1) ) .257LVKHWNRUWLQJVSHUFHQWDJHDOVGHEHWDOLQJYURHJZRUGWJHGDDQ 727'*1LVWKHWRWDOQXPEHURIGD\VXQWLOWKHELOOPXVWEHSDLG.257 '*1LVKHWDDQWDOGDJHQGDWGHNRUWLQJEHVFKLNEDDULV Voorbeeld. 8RQWYDQJWHHQUHNHQLQJPHWGHYRRUZDDUGHQ 1(7:DWNRVWKHWXDOVXJHHQJHEUXLNPDDNWYDQGH NRUWLQJVPRJHOLMNKHLG"

""d * * * Toetsen:

"*

Display:

Beschrijving:

72.000,00

%HUHNHQWGHWHOOHUYDQ GHIRUPXOH +DDNMHVEHSDOHQGH YROJRUGHYDQ EHUHNHQLQJ %HUHNHQWGHNRVWHQYDQ KHWQLHWJHEUXLNPDNHQ YDQGHNRUWLQJDOVHHQ MDDUOLMNVSHUFHQWDJH

98,00

36,73

8: Extra voorbeelden 101


Leningen en hypotheken Enkelvoudige jaarlijkse rente Voorbeeld. (HQJRHGHYULHQGKHHIWHHQOHQLQJQRGLJRPHHQ RQGHUQHPLQJWHEHJLQQHQHQKHHIWXRPHHQOHQLQJYDQYRRU GDJHQJHYUDDJG8OHHQWKHPKHWJHZHQVWHEHGUDJWHJHQ HQNHOYRXGLJHMDDUOLMNVHUHQWHWHEHUHNHQRSEDVLVYDQGDJHQ+RHYHHO UHQWHLVKLMXQDGDJHQVFKXOGLJHQZDWLVKLMXLQWRWDDOVFKXOGLJ"

'H]HIRUPXOHZRUGWJHEUXLNWYRRUKHWEHUHNHQHQYDQHHQHQNHOYRXGLJH MDDUOLMNVHUHQWHRSEDVLVYDQGDJHQLQHHQMDDU 5(17( %('5/(1,1* × 5(17( × 7(50/(1,1*,1'*1 ----------------------------------------------------------------------------------------------------------------------------------------------------

" "d

a Toetsen:

Display:

Beschrijving:

0,10

6ODDWUHQWHRS %HUHNHQWYHUVFKXOGLJGHUHQWH %HUHNHQWWRWDDOYHUVFKXOGLJGH EHGUDJ

7,40 457,40

Continue samenstelling van rente 'HIRUPXOHYRRUKHWEHUHNHQHQYDQGHHIIHFWLHYHUHQWHYRHWELMFRQWLQXH VDPHQVWHOOLQJLV ()) = ( H

(

120 ÷ )

– ) ×

8JDDWDOVYROJWWHZHUNDOVXHHQYUDDJVWXNPHWYRRUWGXUHQGH VDPHQVWHOOLQJZLOWRSORVVHQ %HUHNHQGHMDDUOLMNVHHIIHFWLHYHUHQWHYRHWPHWERYHQVWDDQGHIRUPXOH 8JHEUXLNWyIGH]HHIIHFWLHYHUHQWHYRHWYRRUEHUHNHQLQJHQPHWHHQ MDDUOLMNVHSHULRGH3<5 yIXFRQYHUWHHUWGH]HUHQWHYRHW]RGDW GH]HLQXZEHWDOLQJVSHULRGHYDQWRHSDVVLQJLV,QKHWYROJHQGH YRRUEHHOGLV3<5 ]RGDWXHHQQLHXZH120PRHW EHUHNHQHQPHWEHKXOSYDQGHUHQWHYRHWFRQYHUVLHWRHSDVVLQJZDDUELM 3<5JHOLMNLVDDQ 102 8: Extra voorbeelden


Voorbeeld. 8KHEWRSKHWRJHQEOLNRSHHQUHNHQLQJVWDDQELM 'URRP,QYHVWHULQJHQZDDURSXMDDUOLMNVMDDUOLMNVFRQWLQX JHFXPXOHHUGHUHQWHNULMJW$DQKHWHLQGYDQLHGHUHPDDQGVWRUWX RSGHUHNHQLQJ:DWLVKHWVDOGRQDMDDU"

* " *Z *b * Toetsen:

Display:

Beschrijving:

0,18

'HHOWGHQRPLQDOH UHQWHGRRU 9HUKHIWHWRWGHPDFKW %HUHNHQWGHMDDUOLMNVH HIIHFWLHYHUHQWHYRHW 6ODDWGHHIIHFWLHYH UHQWHYRHWRS 6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ %HUHNHQWGHMDDUOLMNVH QRPLQDOHUHQWHYRRU HHQPDDQGHOLMNVH EHWDOLQJVSHULRGH

1,20 19,72 19,72 12,00 18,14


*U (2 ( /

*ODOVXGH

180,00 –250,00 –4.572,80

297.640,27

BEGIN LQGLFDWRU]LHW

6ODDWKHWDDQWDO PDDQGHQRS 6ODDWGHUHJHOPDWLJH EHWDOLQJRS 6ODDWKHWKXLGLJHVDOGR DOVHHQQHJDWLHYH ZDDUGHRSDOVELMHHQ LQLWLsOHLQYHVWHULQJ %HUHNHQWKHWVDOGRYDQ GHUHNHQLQJQD EHWDOLQJHQJHGXUHQGH MDDUPHWHHQUHQWH YDQGLHFRQWLQX JHFXPXOHHUGZRUGW



Opbrengst van een verdisconteerde (of premie-) hypotheek 'HMDDUOLMNVHRSEUHQJVWYDQHHQYHUGLVFRQWHHUGHRISUHPLHK\SRWKHHNNDQ ZRUGHQEHUHNHQGDOVGHYROJHQGHJHJHYHQVEHNHQG]LMQRRUVSURQNHOLMNH K\SRWKHHNVRP39 UHQWHYRHW,<5 SHULRGLHNHEHWDOLQJ307 EDOORRQEHWDOLQJ)9 HQKHWEHGUDJGDWYRRUGHK\SRWKHHNLVEHWDDOG QLHXZH39 'HQNDDQGHDIVSUDDNRYHUKHWJHEUXLNYDQWHNHQVELMFDVKIORZVEHWDDOGH EHGUDJHQ]LMQQHJDWLHIRQWYDQJHQEHGUDJHQ]LMQSRVLWLHI Voorbeeld. (HQLQYHVWHHUGHUZLOHHQK\SRWKHHNRSQHPHQYDQ WHJHQRYHUHHQSHULRGHYDQMDDU6LQGVGHK\SRWKHHNLVJHQRPHQ ]LMQHUPDDQGHOLMNVHDIEHWDOLQJHQJHGDDQ'HOHQLQJZRUGWDDQKHWHLQG YDQKHWYLMIGHMDDUYROOHGLJEHWDDOGHHQEDOORQEHWDOLQJ :DWLVGH RSEUHQJVWYRRUGHNRSHUDOVGHSULMVYDQGHK\SRWKHHNZDV" Punt 1. %HUHNHQ307/HWHURSGDW)9


*b . *U ( Toetsen:

/ 2


*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWGHUHQWHYRHWRS 6ODDWKHWDDQWDO PDDQGHQRS 6ODDWKHW RRUVSURQNHOLMNHEHGUDJ YDQGHOHQLQJRS 9RHUWKHWEHGUDJLQGDW QDMDDUEHWDDOGPRHW ZRUGHQ %HUHNHQWGH UHJHOPDWLJHEHWDOLQJ

9,00 240,00 –100.000,00

0,00

899,73


Punt 2. 9RHUGHQLHXZHZDDUGHYDQ1LQZDDUPHHZRUGWDDQJHJHYHQ ZDQQHHUGHEDOORQEHWDOLQJJHEHXUW%HUHNHQYHUYROJHQV)9KHWEHGUDJ YDQGHEDOORQEHWDOLQJ

*L2 Toetsen:

*U /

Display:

Beschrijving:

899,73

5RQGWYRRUGH QDXZNHXULJKHLGGH EHWDOLQJRSWZHH GHFLPDOHQDI 6ODDWKHWDDQWDO EHWDOLQJHQWRWGH EDOORQEHWDOLQJRS %HUHNHQWGH EDOORQEHWDOLQJZRUGW ELMGHODDWVWHEHWDOLQJ RSJHWHOG

60,00

88.706,74

Punt 3. 9RHUGHQLHXZHZDDUGHQYDQ1HQ39LQEHUHNHQYHUYROJHQVGH QLHXZH,<5YRRUGHYHUGLVFRQWHHUGHK\SRWKHHNPHWEDOORQEHWDOLQJ

PP ( . Toetsen:

Display:

Beschrijving:

18,00

6ODDWKHWRYHUJHEOHYHQ DDQWDOEHWDOLQJHQRS 6ODDWGHSULMVYDQGH K\SRWKHHNRS %HUHNHQWGHRSEUHQJVW YDQGH]H YHUGLVFRQWHHUGH K\SRWKHHN

–79.000,00 20,72

Jaarlijks percentage voor een lening met kosten +HWMDDUOLMNVSHUFHQWDJH$35QHHPWGHNRVWHQLQDDQPHUNLQJGLH JHZRRQOLMNEHUHNHQGZRUGHQELMKHWDIVOXLWHQYDQHHQK\SRWKHHNHQ ZDDUGRRUGHUHQWHYRHWLQZHUNHOLMNKHLGZRUGWYHUKRRRJG+HWZHUNHOLMNH EHGUDJGDWGHK\SRWKHHNQHPHURQWYDQJW39 ZRUGWHULPPHUVGRRU YHUPLQGHUGWHUZLMOGHSHULRGLHNHEHWDOLQJHQJHOLMNEOLMYHQ'H$35NDQ ZRUGHQEHUHNHQGDOVGHWHUPLMQYDQGHK\SRWKHHN1SHULRGHV GH MDDUOLMNVHUHQWHYRHW,35 GHK\SRWKHHNVRPQLHXZH39 HQKHWEHGUDJ YDQGHNRVWHQEHNHQG]LMQ 8: Extra voorbeelden 105


'HQNDDQGHDIVSUDDNRYHUKHWJHEUXLNYDQWHNHQVELMFDVKIORZVEHWDDOGH EHGUDJHQ]LMQQHJDWLHIRQWYDQJHQEHGUDJHQ]LMQSRVLWLHI Voorbeeld: APR voor een lening waaraan kosten verbonden zijn.

9RRUHHQOHQLQJZRUGWNRVWHQLQUHNHQLQJJHEUDFKWELMKHWDIVOXLWHQ YDQHHQK\SRWKHHN+RHKRRJLVGH$35DOVGHK\SRWKHHNVRP LVHQHHQORRSWLMGKHHIWYDQMDDUPHWHHQMDDUOLMNVHUHQWHYRHWYDQ JHEDVHHUGRSPDDQGHOLMNVHEHWDOLQJHQ" 6WHOGH(LQGPRGXVLQ'UXNRS

*b . *U Toetsen:

/ 2 .


*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWGHUHQWHYRHWRS 6ODDWGHGXXUYDQGH OHQLQJRS 6ODDWKHW RRUVSURQNHOLMNHEHGUDJ YDQGHOHQLQJRS 'HOHQLQJZRUGWLQ MDDUYROOHGLJDIEHWDDOG %HUHNHQWGHEHWDOLQJ 9UDDJWKHWEHGUDJYDQ GHOHQLQJRS 7UHNWKHW NRVWHQSHUFHQWDJHDI %HUHNHQW$35NRVWHQ LQDDQPHUNLQJ JHQRPHQ

8,50 360,00 160.000,00

0,00 –1.230,26 160.000,00 156.800 8,72


Voorbeeld: Lening zonder tussentijdse aflossing. 'H DIVOXLWSURYLVLHYDQHHQMDULJHOHQLQJYDQPHWMDDUOLMNVH UHQWH ]RQGHUWXVVHQWLMGVHDIORVVLQJLV:DWEUHQJWGLWGHNUHGLHWJHYHURS" 1HHPDDQGDWPDDQGHOLMNVHEHWDOLQJHQRYHUGHUHQWHZRUGHQJHGDDQ


*b . *U Toetsen:

(/ 2 .

*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWGHUHQWHYRHWRS 6ODDWGHGXXUYDQGH OHQLQJRS 6ODDWKHW RRUVSURQNHOLMNHEHGUDJ YDQGHOHQLQJRS 9RHUWKHWEHGUDJLQGDW DDQKHWHLQGHYDQGH ORRSWLMGYHUVFKXOGLJG LV%HWDOLQJHQEHVWDDQ DOOHHQXLWUHQWHKHW WRWDDOJHOHHQGHEHGUDJ LVGXVYHUVFKXOGLJG %HUHNHQWGHEHWDOLQJHQ GLHDOOHHQXLWUHQWH EHVWDDQ 9UDDJWKHWEHGUDJYDQ GHOHQLQJRS 7UHNWKHW NRVWHQSHUFHQWDJHDI %HUHNHQW$35

12,00 120,00 1.000.000,00

–1.000.000,00

–10.000,00

1.000.000,00 970.000,00 12,53



Lening met een afwijkende eerste periode 790EHUHNHQLQJHQJDDQRYHUILQDQFLs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oorbeeld. (HQOHQLQJYDQRYHUPDDQGHQKHHIWHHQMDDUOLMNVH UHQWHYDQ$OVGHHHUVWHPDDQGHOLMNVHEHWDOLQJQDGDJHQZRUGW JHGDDQZDWLVGDQGHPDDQGHOLMNVHEHWDOLQJXLWJDDQGHYDQPDDQGHQYDQ GDJHQ"

,QGLWYRRUEHHOGLVGHDIZLMNHQGHHHUVWHSHULRGHGDJHQ 6WHOGH(LQGPRGXVLQ'UXNRS

*b . d" d" Toetsen:


*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 6ODDWGHUHQWHYRHWRS %HUHNHQWGHSHULRGLHNH UHQWHYRHW 9HUPHQLJYXOGLJWPHWHHQGHHO YDQHHQSHULRGH

15,00 1,25 0,67


*i

P / 2

30,00

4.530,00 36,00 0,00 –157,03

%HUHNHQWKHWEHGUDJDDQ HQNHOYRXGLJHUHQWHGDWYRRUGH DIZLMNHQGHSHULRGH YHUVFKXOGLJGLV 7HOWGH]HHQNHOYRXGLJHUHQWHELM GHKXLGLJHZDDUGHRS 6ODDWGHWHUPLMQZDDURYHUGH OHQLQJORRSWRS 9RHUWKHWEHGUDJLQGDWQD EHWDOLQJHQQRJXLWVWDDW %HUHNHQWKHWEHGUDJYDQGH EHWDOLQJ

Een autolening Voorbeeld. 8NRRSWHHQQLHXZHDXWRYRRU8GRHWHHQ DDQEHWDOLQJYDQHQGHUHVWHUHQGHJDDWXILQDQFLHUHQ'H GHDOHUELHGWXWZHHPDQLHUHQZDDURSJHILQDQFLHUGNDQZRUGHQ n (HQMDULJHOHQLQJPHWHHQMDDUOLMNVHUHQWHYDQ n (HQMDULJHOHQLQJPHWHHQMDDUOLMNVHUHQWHYDQHQ NRUWLQJ

,QZHONJHYDOEHWDDOWXPLQGHUYRRUGHDXWR" 6WHOGH(LQGPRGXVLQ'UXNRS

*ODOVXGH

BEGIN LQGLFDWRU]LHW

%HUHNHQGHHHUVWHRSWLH

*b P / . 2 "P Toetsen:

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 6ODDWGHEHNHQGHZDDUGHQRS

36,00 12,500.00 0,00 3,50 –366,28 –13.185,94

6ODDWGHHHUVWHUHQWHRS %HUHNHQWGHEHWDOLQJ %HUHNHQWGHWRWDOHUHQWHHQ KRRIGVRP 8: Extra voorbeelden 109


%HUHNHQGHWZHHGHRSWLH

. 2 "P Toetsen:

Display:

Beschrijving:

11.500,00

6ODDWEHGUDJYDQOHQLQJ PLQGHNRUWLQJRS 6ODDWGHWZHHGHUHQWH RS %HUHNHQWGHEHWDOLQJ %HUHNHQWGHWRWDOH UHQWHHQKRRIGVRP

9,50 –368,38 –13.261,64

'HHHUVWHRSWLHNRVWLHWVPLQGHU

“Canadese hypotheek” %LM&DQDGHVHK\SRWKHNHQ]LMQGHEHWDOLQJVSHULRGHVHQGH VDPHQVWHOOLQJVSHULRGHVQLHWJHOLMN'HUHQWHZRUGWKDOIMDDUOLMNV VDPHQJHVWHOGWHUZLMOEHWDOLQJHQPDDQGHOLMNVJHEHXUHQ$OVXGH790 PRJHOLMNKHLGYDQGH+3%,,ZLOWJHEUXLNHQPRHWXHHQ&DQDGHVH K\SRWKHHNIDFWRUEHUHNHQHQGLWLVHHQDDQJHSDVWHUHQWHYRHW HQGH]HLQ,<5 RSVODDQ 0HHULQIRUPDWLHRYHUUHQWHYRHWFRQYHUVLHVYLQGWXRS ´5HQWHYRHWFRQYHUVLHVµRSSDJLQD Voorbeeld. :HONHPDDQGHOLMNVHEHWDOLQJLVQRGLJRPHHQ&DQDGHVH K\SRWKHHNYDQRYHUMDDUWHDPRUWLVHUHQDOVGHMDDUOLMNVH UHQWHYRHWLV"

* *b *Z *b * Toetsen:


Display:

Beschrijving:

12,00 2,00

6ODDWKHWEHNHQGHQRPLQDOH SHUFHQWDJHHQKHWDDQWDO VDPHQVWHOOLQJVSHULRGHV %HUHNHQWGHMDDUOLMNVHHIIHFWLHYH UHQWHYRHW 6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ %HUHNHQWGH&DQDGHVH K\SRWKHHNIDFWRUDDQJHSDVWH UHQWHYRHW

12,36 12,00 11,71


/*U 2

130.000 360,00 –1.308,30

6ODDWDQGHUHEHNHQGHZDDUGHQ YDQGHK\SRWKHHNRS %HUHNHQWGHPDDQGHOLMNVH EHWDOLQJYRRUGH&DQDGHVH K\SRWKHHN

TVM-berekeningen voor “wat als...”-scenario’s (pQYDQGHPHHVWZDDUGHYROOHDVSHFWHQYDQGH790WRHSDVVLQJYDQGH +3%,,LVKHWJHPDNZDDUPHHGH]HWRHSDVVLQJNDQZRUGHQJHEUXLNW YRRUEHUHNLQJHQLQYHUEDQGPHW´ZDWDOVµVFHQDULR·VVLPXODWLHV(HQHUJ FRXUDQWHVLPXODWLHLVGHYROJHQGH´:DWDOVGHUHQWHYRHWYHUDQGHUWLQ«" 2SZHONHPDQLHUEHwQYORHGWGDWPLMQEHWDOLQJ"µ1DGDWXHHQEHWDOLQJ KHEWEHUHNHQGGLHRSHHQEHSDDOGHUHQWHYRHWLVJHEDVHHUGKRHIWXRP RSGH]HYUDDJDQWZRRUGWHNULMJHQDOOHHQGHQLHXZHUHQWHYRHWLQWH YXOOHQHQ307RSQLHXZWHEHUHNHQHQ ,QHHQSDDUYRRUEHHOGHQHHUGHULQGH]HKDQGOHLGLQJKDGGHQZHKHW JHEUXLNWYRRUZDWDOVVFHQDULR·VDOHYHQDDQJHVWLSWPDDUKLHUYROJW HHQPHHUXLWJHZHUNWYRRUEHHOG Voorbeeld. 8VWDDWRSKHWSXQWRPYRRUGHDDQNRRSYDQHHQ YDNDQWLHKXLVHHQK\SRWKHHNYDQRYHUMDDUWHRQGHUWHNHQHQ 'HMDDUOLMNVHQRPLQDOHUHQWHYRHWLV Deel 1. +RHJURRW]LMQXZEHWDOLQJHQDDQKHWHLQGYDQGHPDDQG"


*b . *U / 2 Toetsen:

*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

12,00

6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWGHEHNHQGH ZDDUGHQRS

735.000,00 11,20 360,00 0,00 –7.110,88

%HUHNHQWGHEHWDOLQJ



Deel 2. 'HVDODULVVHQYDQXZEHGULMIZRUGHQJHZRRQOLMNHHQVLQGHWZHH ZHNHQRSYULMGDJEHWDDOG'HEDQNJDDWHUPHHDNNRRUGYDQLHGHUH VDODULVXLWNHULQJRSWHQHPHQRQJHYHHUGHKHOIWYDQHHQ PDDQGHOLMNVHEHWDOLQJ HQGHEHWDOLQJVSHULRGHGDDUELMDDQWHSDVVHQ VDPHQVWHOOLQJVSHULRGHVSHUMDDU :DWLVGHQLHXZHORRSWLMGYDQGHOHQLQJ"

(2 *b P *U

–3.555,00 26,00

514,82

19,80

9RHUWGHQLHXZH EHWDOLQJLQ 6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ RSWZHHZHNHOLMNVH EHWDOLQJHQ %HUHNHQWKHWDDQWDO WZHHZHNHOLMNVH EHWDOLQJHQ *HHIWKHWDDQWDOMDUHQ ZHHUGDWQRGLJLVRP GHOHQLQJDIWHORVVHQ

Deel 3. :DWJHEHXUWHUDOVXPDDQGHOLMNVHEHWDOLQJHQ]RXGRHQ]RDOVLQ GHHOPDDU]RXRSWHUHQYRRUORRSWLMGYDQMDDU"+RHJURRW]RXLQGDW JHYDOGHPDDQGVRP]LMQ":DW]RXHUWRWDDODDQUHQWHEHWDDOGZRUGHQELM GLWFRQWUDFW"

*b *U 2 "P Toetsen:


Display:

Beschrijving:

12,00

6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWGHQLHXZH ORRSWLMGRS %HUHNHQWGHEHWDOLQJELM HHQNRUWHUHORRSWLMG %HUHNHQWGHWRWDOH EHWDOLQJ *HHIWGHWRWDOHUHQWH ZHHUGLHYRRUKHW FRQWUDFWZRUGWEHWDDOG

180,00 –8.446,53 –1.520.374,70 –785.374,70


Sparen Sparen voor hogere studies 6WHOGDWXQXYRRU]LHQLQJHQWUHIWRPLQGHWRHNRPVWHHQDDQWDOXLWJDYHQ WHGRHQ(HQYRRUEHHOGKLHUYDQLVVSDUHQYRRUGHKRJHUHVWXGLHVYDQXZ NLQGHUHQ2PWHNXQQHQEHSDOHQKRHYHHOXSHUSHULRGHPRHWVSDUHQ PRHWXZHWHQZDQQHHUXKHWJHOGQRGLJKHEWKRHYHHOXQRGLJKHEWHQ WHJHQZHONHUHQWHYRHWXXZVSDDUJHOGNXQWLQYHVWHUHQ Voorbeeld. 8ZRXGVWHGRFKWHUJDDWRYHUMDDUQDDUGHXQLYHUVLWHLWHQX EHJLQWQXWHVSDUHQRPKDDURSOHLGLQJWHEHWDOHQ=H]DOJHGXUHQGHYLHU MDDUDDQKHWEHJLQYDQHONMDDUQRGLJKHEEHQ+HWIRQGVZRUGW XLWJH]HWWHJHQSHUMDDUPDDQGHOLMNVVDPHQJHVWHOGHUHQWHHQXZLOW PDDQGHOLMNVHEHWDOLQJHQGRHQWHEHJLQQHQDDQKHWHLQGYDQGHORSHQGH PDDQG'HVWRUWLQJHQZRUGHQJHVWRSWDOV]LMKDDUVWXGLHVEHJLQW+RHYHHO PRHWXSHUPDDQGVWRUWHQ"

'LWSUREOHHPZRUGWLQWZHHVWDSSHQRSJHORVW%HUHNHQHHUVWKHWEHGUDJ GDWXQRGLJKHEWDOV]LMQDDUGHXQLYHUVLWHLWJDDW%HJLQPHWHHQ UHQWHFRQYHUVLHGLWLVQRGLJRPGDWGHUHQWHPDDQGHOLMNVZRUGW VDPHQJHVWHOG $15.000

Jaar 1

Toetsen:

* *b

I/YR = 9%

Jaar 2

Jaar 3

*ODOVXGH

Display:


*Z

9,00 12,00

9,38

Jaar 4

Beschrijving: BEGIN LQGLFDWRUQLHW]LHW

6ODDWGHMDDUOLMNVHQRPLQDOH UHQWHRS 6ODDWKHWDDQWDOSHULRGHVRS ZDDULQPHWGH]HQRPLQDOHUHQWH JHFXPXOHHUGZRUGW %HUHNHQWGHMDDUOLMNVHHIIHFWLHYH UHQWHYRHW 8: Extra voorbeelden 113


$OVGHUHQWHPDDUppQNHHUSHUMDDUZRUGWVDPHQJHVWHOG]LMQGHHIIHFWLHYH UHQWHHQGHQRPLQDOHUHQWHJHOLMN

.

9,38

6WHOGH%HJLQPRGXVLQ'UXNRS ]LHW

*b 2 P /

*ODOVXGH

1,00 15.000,00 4,00 0,00 –52.713,28

6ODDWGHHIIHFWLHYHUHQWH DOVMDDUOLMNVHUHQWHRS

BEGIN LQGLFDWRUQLHW

6WHOWppQEHWDOLQJSHU MDDULQ 6ODDWGHMDDUOLMNVH RSQDPHRS 6ODDWKHWDDQWDO RSQDPHVRS 6ODDWKHWVDOGRQDYLHU MDDURS 6ODDWKHWEHGUDJRSGDW QRGLJLVDOVXZGRFKWHU DDQKDDURSOHLGLQJ EHJLQW

*HEUXLNYHUYROJHQVGH]H39DOVGH)9YDQKHWYROJHQGH FDVKIORZGLDJUDPHQEHUHNHQGH307

FV van vorige berekening

I/YR = 9% 1

2

3

PMT = ?


4

...

142

143 144



(/ *b P . 2

*ODOVXGH

BEGIN LQGLFDWRU]LHW

6ODDWKHWEHGUDJRSGDW XQRGLJKHEW 6ODDWKHWEHGUDJRS ZDDUPHHXEHJLQW 6WHOWKHWDDQWDO EHWDOLQJHQSHUMDDULQ 6ODDWKHWDDQWDO VWRUWLQJHQRS 6ODDWGHUHQWHYRHWRS %HUHNHQWZDWHU PDDQGHOLMNVJHVWRUW PRHWZRUGHQ

52.713,28 0,00 12,00 144,00 9,00 –204,54

Kapitaaltoename die onbelast is todat deze wordt opgenomen 0HWGH790WRHSDVVLQJNXQWXGHWRHNRPVWLJHZDDUGHYDQHHQ EHODVWLQJYULMHRIXLWJHVWHOGHEHODVWLQJUHNHQLQJEHSDOHQ+HWKDQJWYDQGH EHODVWLQJZHWHQXZLQNRPHQDIRI]RZHOGHUHQWHDOVGHKRRIGVRP EHODVWLQJYULM]LMQ8NXQWEHLGHJHYDOOHQRSORVVHQ 'HNRRSNUDFKWYDQGLHWRHNRPVWLJHZDDUGHLVDIKDQNHOLMNYDQGHLQIODWLH HQGHORRSWLMGYDQGHUHNHQLQJ Voorbeeld. 8RYHUZHHJWHHQUHNHQLQJWHRSHQHQZDDUYDQGHEHODVWLQJ ZRUGWXLWJHVWHOGPHWHHQGLYLGHQGYDQ$OVXJHGXUHQGHMDDU DDQKHWEHJLQYDQLHGHUMDDULQYHVWHHUWKRHYHHOVWDDWHUGDQRSGH UHNHQLQJELMSHQVLRQHULQJ"+RHYHHOKHEWXGDQLQWRWDDOJHVWRUW"+RHYHHO UHQWHKHEWXJHNUHJHQ":DWLVGHZDDUGHYDQXZUHNHQLQJQDEHODVWLQJHQ DOVXQDSHQVLRQHULQJEHODVWLQJEHWDDOW"*DHUYDQXLWGDWDOOHHQGH UHQWHZRUGWEHODVWHQGDWGHKRRIGVRPYRRUKHWVWRUWHQLVEHODVW :DWLV GHNRRSNUDFKWYDQGHUHNHQLQJXLWJHGUXNWLQGHKXLGLJHZDDUGHYDQGH GROODUHQJHUHNHQGHPHWHHQLQIODWLHYDQ"


*ODOVXGH

BEGIN LQGLFDWRUQLHW



*b P . (2 / Toetsen:

2"P

/ " ( / / .2


Display:

Beschrijving:

1,00

6WHOWppQEHWDOLQJSHU MDDULQ 6ODDWKHWDDQWDO SHULRGHVHQGH UHQWHYRHWRS 6ODDWKHWEHGUDJRS ZDDUPHHXEHJLQW 6ODDWGHMDDUOLMNVH EHWDOLQJRS %HUHNHQWKHWEHGUDJ GDWELMSHQVLRQHULQJRS GHUHNHQLQJVWDDW %HUHNHQWKHWWRWDOH EHGUDJGDWXRSKHW PRPHQWYDQ SHQVLRQHULQJJHVWRUW KHEW %HUHNHQWGHUHQWHGLH GHUHNHQLQJKHHIW RSJHEUDFKWELM SHQVLRQHULQJ %HUHNHQWEHODVWLQJ RYHUGHUHQWH %HUHNHQW)9QD EHODVWLQJHQ 6ODDWWRHNRPVWLJH ZDDUGHQDEHODVLQJHQ LQ)9RS %HUHNHQW)9GH KXLGLJHZDDUGHYDQGH NRRSNUDFKWQD EHODVWLQJHQXLWJDDQGH YDQLQIODWLH

35,00 8,18 0,00 –2.000,00 387.640,45

–70.000,00

317.640,45

47.646,07 339.994,39 339.994,39

–86.159,84


Waarde van een belastbare pensioenrekening %LMGLWSUREOHHPZRUGWGH790WRHSDVVLQJJHEUXLNWRPGHWRHNRPVWLJH ZDDUGHYDQHHQEHODVWEDUHSHQVLRHQUHNHQLQJWHEHUHNHQHQZDDURSPHW LQJDQJYDQYDQGDDJUHJHOPDWLJHMDDUOLMNVHEHWDOLQJHQZRUGHQJHGDDQ %HJLQPRGXV +HWEHGUDJGDWMDDUOLMNVDDQEHODVWLQJZRUGWEHWDDOGZRUGW XLWGHUHNHQLQJJHKDDOG*DHUYDQXLWGDWGHVWRUWLQJHQUHHGVEHODVW]LMQ Voorbeeld. $OVXLHGHUMDDUJHGXUHQGHMDDULQYHVWHHUWHQ GLYLGHQGNULMJWGDWDOVQRUPDDOLQNRPHQEHODVWZRUGWKRHYHHOVWDDWHUGDQ RSGHUHNHQLQJELMSHQVLRQHULQJ"*DHUYDQXLWGDWHUGLYLGHQGSHU MDDUZRUGWEHWDDOGKHWEHODVWLQJVSHUFHQWDJHLVHQGDWGHEHWDOLQJHQ YDQGDDJEHJLQQHQ+RHJURRWLVGHNRRSNUDFKWYDQGDWEHGUDJLQ KHGHQGDDJVHGROODUVXLWJDDQGHYDQHHQLQIODWLHYDQ"


*b P

Toetsen:

. (2 / .2

*ODOVXGH

BEGIN LQGLFDWRUQLHW

Display:

Beschrijving:

1,00

6WHOWppQEHWDOLQJSHU MDDULQ 6ODDWDDQWDO EHWDOLQJVSHULRGHVRS WRWDDQKHWSHQVLRHQ %HUHNHQWGHUHQWHYRHW YHUPLQGHUGPHWKHW EHODVWLQJSHUFHQWDJH 6ODDWGHDDQJHSDVWH UHQWHYRHWRS 6ODDWKHWEHGUDJRS ZDDUPHHXEHJLQW 6ODDWGHMDDUOLMNVH EHWDOLQJRS %HUHNHQWKHWEHGUDJ GDWELMSHQVLRQHULQJRS GHUHNHQLQJVWDDW %HUHNHQWGHFRQWDQWH ZDDUGHYDQGH NRRSNUDFKW)9ELMHHQ LQIODWLHYDQ

35,00

5,89

5,89 0,00 –3.000,00 345.505,61

–87.556,47



Voorbeelden met cashflow Wrap-aroundhypotheken (HQZUDSDURXQGK\SRWKHHNLVHHQFRPELQDWLHYDQRSQLHXZILQDQFLHUHQ YDQHHQK\SRWKHHNHQOHQHQRSEDVLVYDQYDVWJRHGHLJHQGRP*HZRRQOLMN ]LMQGHWZHHRQEHNHQGHJURRWKHGHQLQGHZUDSDURXQGK\SRWKHHNGH QLHXZHEHWDOLQJHQKHWUHQGHPHQWYDQGHNUHGLHWJHYHU2PGLWSUREOHHP RSWHORVVHQPRHWXJHEUXLNPDNHQYDQGH790WRHSDVVLQJqQGH FDVKIORZWRHSDVVLQJ Voorbeeld. 8PRHWQRJPDDQGHOLMNVHEHWDOLQJHQYDQGRHQRS XZK\SRWKHHNYDQZDDUQRJHHQVDOGRYDQRSVWDDW8 ZLOWKLHUYDQJHEUXLNPDNHQHQHHQH[WUDOHQHQYRRUHHQDQGHUH LQYHVWHULQJ8YLQGWLHPDQGGLHXNUHGLHWZLOYHUOHQHQWHJHQXZ YDVWJRHGYHUPRJHQYRRUHHQEHGUDJYDQWHJHQRYHU MDDU+RHKRRJ]LMQXZQLHXZHEHWDOLQJHQHQZDWLVKHWUHQGHPHQWGDWGH NUHGLHWJHYHURSGH]HK\SRWKHHNNULMJW"

'HEHUHNHQLQJYDQGHEHWDOLQJLVHHQJHZRQH790EHWDOLQJEHUHNHQLQJ ZDDUELMKHWQLHXZHEHGUDJDOV39ZRUGWJHEUXLNW 6WHOGH(LQGPRGXVLQ'UXNRS

*& *b Toetsen:

. / *U 2 118 8: Extra voorbeelden

*ODOVXGH

BEGIN LQGLFDWRU]LHW

Display:

Beschrijving:

0,00

:LVWDOOHUHJLVWHUV 6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 6ODDWEHGUDJYDQGHOHQLQJRS ZDDURSXZQLHXZHOHQLQJLV JHEDVHHUG 6ODDWGHUHQWHYRHWRS 6ODDWKHWODDWVWHVDOGRRS 6ODDWKHWWRWDDODDQWDO PDDQGHOLMNVHEHWDOLQJHQRS %HUHNHQWGHQLHXZHEHWDOLQJ

12,00 82.510,22

9,50 0,00 180,00 –861,59


9RHUYHUYROJHQVGHFDVKIORZVLQGLHGHZUDSDURXQGK\SRWKHHNYDQXLWKHW RRJSXQWYDQGHNUHGLHWJHYHUYROOHGLJYRRUVWHOOHQRPKHWUHQGHPHQWYDQ GHNUHGLHWJHYHUWHEHUHNHQHQ 47.510,22 861,59

. 1

2

3

.

.

.

4

82

83

.

.

84

180

-754,00 -82.510,22

:DQQHHUXERYHQVWDDQGHFDVKIORZVJURHSHHUW]LHWXGDW &) ² ² &)

²

1

&)

1

²

(, 2(, *C 2(, *C *9 Toetsen:

Display:

Beschrijving:

CF0 –35.000,00

9RHUWLQDOVEHGUDJYDQ GHOHQLQJLQ 9RHUWGHQHWWREHWDOLQJLQYRRU GHHHUVWHPDDQGHQ 9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW 9RHUWGHQHWWREHWDOLQJLQYRRU GHYROJHQGHPDDQGHQ 9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW %HUHNHQWGHMDDUOLMNVH RSEUHQJVW

CF1 107,59 n1 82,00 CF2 861,59 n2 98,00 10,16



Netto toekomstige waarde 'HQHWWRWRHNRPVWLJHZDDUGHNDQEHUHNHQGZRUGHQGRRUPHWGH790 WRHWVHQGHQHWWRKXLGLJHZDDUGH139 LQKHWFDVKIORZGLDJUDPQDDU UHFKWVWHVFKXLYHQ Voorbeeld: Waarde van een fonds. 8KHEWGHDIJHORSHQWZHHMDDUGH

YROJHQGHVWRUWLQJHQJHGDDQLQHHQJHOGPDUNWIRQGVGDWRSEUHQJW :DWLVKHWKXLGLJHVDOGRYDQXZUHNHQLQJ"

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 -3.000 -12.000

I/YR = 8,8%


*& *b (, , *C (, *C ,*C (, Toetsen:


-2.000

-7.500

Huidige datum

*ODOVXGH

Display: 12,00 CF0 –12.000,00 CF1 0,00 n1 2,00 CF2 –3.000,00 n2 3,00 n3 9,00 CF4 –7.500,00

BEGIN LQGLFDWRU]LHW

Beschrijving:

:LVWDOOHUHJLVWHUV 6WHOWKHWDDQWDOEHWDOLQJHQSHU MDDULQ 9RHUWGHHHUVWHFDVKIORZLQ 9RHUWKHWEHGUDJLQYDQJURHS 9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW 9RHUWKHWEHGUDJLQYDQJURHS 9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW 9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW 9RHUWFDVKIORZJURHSLQ


,*C (, . *N P 2 /

n5 3,00 CF6 –2.000,00 8,80 –29.203,14

24,00

9RHUWLQKRHYDDNGHEHWDOLQJ YRRUNRPW 9RHUWFDVKIORZJURHSLQ 6ODDWGHMDDUOLMNVHUHQWHYRHWRS %HUHNHQWGHQHWWRFRQWDQWH ZDDUGH139 GLHDXWRPDWLVFK DOV39ZRUGWRSJHVODJHQ 6ODDWGHEHNHQGHZDDUGHQRS

0,00 34.800,58

%HUHNHQWGHQHWWRWRHNRPVWLJH ZDDUGH




A Hulp, Batterijen en Service +HZOHWW3DFNDUG]LHWKHWDOV]LMQWDDNRPEOLMYHQGHRQGHUVWHXQLQJWH ELHGHQ8NXQWYDQRQV&DOFXODWRU6XSSRUW'HSDUWPHQWDQWZRRUGNULMJHQ RSYUDJHQRYHUKHWJHEUXLNYDQGHFDOFXODWRU /HHVHHUVW´$QWZRRUGHQRSGHPHHVWYRRUNRPHQGHYUDJHQµYRRUGDWX PHWRQVFRQWDFWRSQHHPW2Q]HHUYDULQJLVGDWYHOHYDQRQ]HNODQWHQ GH]HOIGHYUDJHQKHEEHQRYHURQ]HSURGXFWHQ$OVXJHHQDQWZRRUGRS XZYUDJHQYLQGWNXQWX]LFKPHWRQVLQYHUELQGLQJVWHOOHQGRRUKHWDGUHV RIWHOHIRRQQXPPHUWHJHEUXLNHQGDWRSGHELQQHQNDQWYDQKHW DFKWHUEODGLVYHUPHOG

Antwoorden op de meest voorkomende vragen Q: :HUNWGHFDOFXODWRUJRHGRIGRHLN]HOILHWVYHUNHHUG"+RHNDQLN

YDVWVWHOOHQRIGHFDOFXODWRUJRHGZHUNW"

A: =LH´9DVWVWHOOHQRIGHFDOFXODWRUVHUYLFHQRGLJKHHIWµRSSDJLQD Q: ,QPLMQJHWDOOHQVWDDQNRPPD·VLQSODDWVYDQSXQWHQRPGHGHFLPDOHQ

DDQWHJHYHQ+RHNDQLNGHSXQWHQWHUXJNULMJHQ"

* SDJLQD

A: 'UXNRS

Q: +RHNDQLNKHWDDQWDOGHFLPDOHQYHUDQGHUHQGDWGH+3 %,,LQGH

GLVSOD\WRRQW"

*JHYROJGGRRUKHWDDQWDOGHFLPDOHQGDWXZHQVW

A: 'UXNRS

SDJLQD

A: Hulp, Batterijen en Service 123


Q: :DWEHWHNHQWHHQ´(µLQHHQJHWDOELMYRRUEHHOG(² " A: ([SRQHQWYDQWLHQELMYRRUEHHOGï² =LH

´:HWHQVFKDSSHOLMNHQRWDWLHµRSSDJLQD

Q: :DDURPNULMJLNYHUNHHUGHDQWZRRUGHQRIGHPHOGLQJno SoLution ELM KHWJHEUXLNYDQ790" A: &RQWUROHHURIXELMYLHUYDQGHYLMI790ZDDUGHQHHQZDDUGHKHEW LQJHYRHUGYRRUGDWXGHYLMIGHRSORVWRRNDOVppQYDQGHZDDUGHQQXOLV 9HUJHHWQLHWHHQQXOYRRU RSWHVODDQDOVXHHQOHQLQJYROOHGLJDIORVW +HWZLVVHQYDQDOOHUHJLVWHUV YRRUGDWXXZEHNHQGHZDDUGHQ LQYRHUWJHHIWKHW]HOIGHHIIHFW&RQWUROHHURIGHFDOFXODWRULQGHMXLVWH EHWDOLQJVPRGXVVWDDW%HJLQRI(LQGPRGXV HQGDW3<5MXLVWLV LQJHVWHOG

/ *&

Q: +RHNDQLNKHWWHNHQYDQHHQJHWDOLQHHQOLMVWPHWFDVKIORZV

YHUDQGHUHQ"

A: 8PRHWGHLQJHYRHUGHFDVKIORZYHUDQGHUHQ=LH´&DVKIORZVEHNLMNHQ HQYHUYDQJHQµRSSDJLQD Q: :DWEHWHNHQWPEND LQGHGLVSOD\" A: (HQUHNHQNXQGLJHEHZHUNLQJZRUGWXLWJHYRHUG Q: :DWEHWHNHQWINPUT LQGHGLVSOD\" A:8KHEWRSGH

0WRHWVJHGUXNWSDJLQD

Q: :DDURPLV,55<5JURWHUGDQLNYHUZDFKWWH" A: 'LWLV,55SHUMDDU2PHHQ,55SHUSHULRGHWHNULMJHQPRHWX,55 <5GHOHQGRRU3<5

124 A: Hulp, Batterijen en Service


Omgevingsfactoren 2PGLWSURGXFWEHWURXZEDDUWHODWHQZHUNHQPRHWXYHUPLMGHQGDWGH FDOFXODWRUQDWZRUGWHQPRHWXGHYROJHQGHOLPLHWHQTXDWHPSHUDWXXUHQ YRFKWLJKHLGLQDFKWQHPHQ n 7HPSHUDWXXUELMJHEUXLNWRW&WRW) n %HZDDUWHPSHUDWXXU²WRW&²WRW) n 9RFKWLJKHLGELMJHEUXLNHQRSVODJUHODWLHYHYRFKWLJKHLGELM PD[LPDDO&) Geluidssterkte. ,QGHQRUPDOHKRXGLQJELMQRUPDDOJHEUXLNSHU,62

/S$G%

Voeding en Batterijen 'HFDOFXODWRUZRUGWJHYRHGGRRUWZHHYROWOLWKLXPNQRRSFHOEDWWHULMHQ *HEUXLNHQNHOQLHXZHNQRRSFHOEDWWHULMHQDOVXGHEDWWHULMHQYHUYDQJW %HLGHEDWWHULMHQPRHWHQWHJHOLMNYHUYDQJHQZRUGHQ *HEUXLNJHHQRSODDGEDUHEDWWHULMHQ

Batterij-indicator $OVGHLQGLFDWRU ]LFKWEDDULVEHWHNHQWGLWGDWXGHEDWWHULMHQ]R VSRHGLJPRJHOLMNPRHWYHUYDQJHQ'HLQGLFDWRUIOLNNHUWDOVGH VWURRPVWHUNWHWHODDJZRUGW $OVGHEDWWHULMLQGLFDWRUDDQJDDWHQGHGLVSOD\]ZDNNHUZRUGWYHUOLFKWNDQ KHW]LMQGDWXJHJHYHQVNZLMWUDDNW$OVJHJHYHQVYHUORUHQJDDQWHQJHYROJH YDQWHODJHVWURRPVWHUNWH]LHWXGHPHOGLQJAll Clear

Batterijspecificaties 8Z+3FDOFXODWRUJHEUXLNWWZHHOLWKLXPEDWWHULMHQ&5



Batterijen plaatsen =RUJGDWXWZHHQLHXZH&5EDWWHULMHQKHEW5DDNEDWWHULMHQ HQNHODDQGHUDQGDDQ9HHJHONHEDWWHULMVFKRRQPHWHHQQLHW SOXL]HQGHGRHNRPYXLOHQYHWWHYHUZLMGHUHQ &RQWUROHHURIGHFDOFXODWRUXLWVWDDW8YHUOLHVWGHLQKRXGYDQKHW JHKHXJHQDOVXGHEDWWHULMHQYHUYDQJWVFKULMIGXVGHJHJHYHQVRSGLH XRSJHVODJHQKHEWHQQRGLJKHEWYRRUODWHUJHEUXLN 'UDDLGHFDOFXODWRURPHQYHUZLMGHUGHNOHSYDQGHEDWWHULMKRXGHU

Toegang tot de batterijhouder

9HUZLMGHUEHLGHEDWWHULMHQ

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.

3ODDWVGHQLHXZHEDWWHULMHQHQFRQWUROHHURIKHWSRVLWLHIWHNHQ RSHONHEDWWHULMQDDUEXLWHQZLMVW 3ODDWVGHNOHSYDQGHEDWWHULMKRXGHUWHUXJ 'UXNRS

1

$OVGHFDOFXODWRUQLHWDDQJDDWYROJGDQGHSURFHGXUHVLQGHYROJHQGH SDUDJUDDI 126 A: Hulp, Batterijen en Service


Vaststellen of de calculator service nodig heeft *HEUXLNGH]HULFKWOLMQHQRPWHEHSDOHQRIGHFDOFXODWRUVHUYLFHQRGLJ KHHIW$OVGHSURFHGXUHVEHYHVWLJHQGDWGHFDOFXODWRUQLHWQDDUEHKRUHQ ZHUNWOHHVGDQGHSDUDJUDDI´$OVGHFDOFXODWRUVHUYLFHQRGLJKHHIWµRS SDJLQD n De calculator is niet aan te krijgen (er verschijnt niets in de display):

'H]HVLWXDWLHEHWHNHQWPHHVWDOGDWGHEDWWHULMHQOHHJ]LMQ3ODDWV QLHXZHEDWWHULMHQ $OVGHFDOFXODWRUQRJVWHHGVQLHWDDQWHNULMJHQLVDOVXRS GUXNW VWHOGHFDOFXODWRURSQLHXZLQ]LHYHUGHU HQLQGLHQQRGLJ :LVKHWJHKHXJHQ]LHYHUGHU 'HPHOGLQJ All Clear ]RXQXPRHWHQYHUVFKLMQHQ$OVGLWQLHWKHW JHYDOLVGDQLVVHUYLFHQRGLJ

1

De calculator opnieuw instellen

'UDDLGHFDOFXODWRURPHQYHUZLMGHUGHNOHSYDQGH EDWWHULMKRXGHU 'UXNKHWXLWHLQGHYDQHHQSDSHUFOLSLQKHWNOHLQHURQGHJDW WXVVHQGHEDWWHULMHQ'UXNGHFOLS]RYHUPRJHOLMNLQKHWJDW +RXGH]HppQVHFRQGHLQJHGUXNWHQYHUZLMGHUGDQGHFOLS 'UXNRS $OVGHFDOFXODWRUQRJVWHHGVQLHWUHDJHHUWZLVGDQKHWJHKHXJHQ ]LHYHUGHU HQKHUKDDOVWDSSHQWRWQRJHHQNHHU

1

1

Het geheugen van de calculator wissen

+RXGGH WRHWVLQJHGUXNW +RXGYHUYROJHQV]RZHOGH DOVGH WRHWVLQJHGUXNW /DDWGHGULHWRHWVHQORV +HWJHKHXJHQLVJHZLVWHQGHPHOGLQJAll Clear]RXQX]LFKWEDDU PRHWHQ]LMQ

P

/



n De calculator reageert niet op op het aanslaan van toetsen (er gebeurt niets als u op de toetsen drukt):

6WHOGHFDOFXODWRURSQLHXZLQzie boven HQLQGLHQQRGLJ ZLVKHWJHKHXJHQzie boven 'HPHOGLQJ All Clear ]RXQXPRHWHQYHUVFKLMQHQ$OVGLWQLHWKHW JHYDOLVGDQLVVHUYLFHQRGLJ n De calculator reageert wel op toetsaanslagen maar u vermoedt dat hij toch niet werkt zoals het hoort:

+HWLVPRJHOLMNGDWXHHQIRXWKHEWJHPDDNWELMKHWEHGLHQHQ YDQGHFDOFXODWRU+HUOHHVGHWRHSDVVHOLMNHGHOHQYDQGH KDQGOHLGLQJHQFRQWUROHHU´$QWZRRUGHQRSGHPHHVW YRRUNRPHQGHYUDJHQµRSSDJLQD 1HHPFRQWDFWRSPHWKHW&DOFXODWRU6XSSRUW'HSDUWPHQW+HW DGUHVHQWHOHIRRQQXPPHUVWDDQDDQGHELQQHQ]LMGHYDQKHW DFKWHUEODG

Beperkt garantiebewijs voor één jaar Wat onder de garantie valt +HZOHWW3DFNDUGJHHIWJDUDQWLHRSGHFDOFXODWRUPHWXLW]RQGHULQJYDQGH EDWWHULMHQRIVFKDGHYHURRU]DDNWGRRUGHEDWWHULMHQ WHQDDQ]LHQYDQ PDWHULDDOGHIHFWHQHQRQWRHUHLNHQGYDNPDQVFKDSJHGXUHQGHppQMDDUQDGHGDWXPYDQ RRUVSURQNHOLMNHDDQNRRS$OVXGHFDOFXODWRUYHUNRRSWRIZHJJHHIWJDDWGH JDUDQWLHDXWRPDWLVFKRYHURSGHQLHXZHHLJHQDDUHQEOLMIWJHOGLJ JHGXUHQGHGHRRUVSURQNHOLMNHSHULRGHYDQppQMDDU*HGXUHQGHGH JDUDQWLHWHUPLMQNXQWXHHQSURGXFWGDWPDQNHPHQWHQYHUWRRQWGRRURQV NRVWHORRVODWHQUHSDUHUHQRIYHUYDQJHQRSYRRUZDDUGHGDWXKHW EHWUHIIHQGHSURGXFWYROGRHQGHJHIUDQNHHUGDDQHHQVHUYLFHGLHQVWYDQ +HZOHWW3DFNDUGUHWRXUQHHUW9HUYDQJLQJNDQJHVFKLHGHQGRRUHHQ QLHXZHURIJHOLMNZDDUGLJPRGHORIHHQPRGHOPHWEHWHUHIXQFWLRQDOLWHLW 'LWJDUDQWLHEHZLMVJHHIWXEHSDDOGHZHWWHOLMNHUHFKWHQ7HYHQVNXQWX EHSDDOGHUHFKWHQKHEEHQGLHSHUODQGHQ]HOIVELQQHQHHQODQGNXQQHQ YHUVFKLOOHQ



Wat niet onder de garantie valt %DWWHULMHQHQGRRUEDWWHULMHQYHURRU]DDNWHVFKDGHZRUGHQQLHWGRRUGH +HZOHWW3DFNDUGJDUDQWLHJHGHNW5DDGSOHHJXZOHYHUDQFLHURYHUJDUDQWLH RSEDWWHULMHQHQZDWEHWUHIWOHNNDJHV 'LWJDUDQWLHEHZLMVLVQLHWJHOGLJZDQQHHUKHWSURGXFWEHVFKDGLJGLVGRRU HHQRQJHYDORIRQGHVNXQGLJJHEUXLNWRIWHQJHYROJHYDQRQGHUKRXGRI DDQSDVVLQJGRRUHHQQLHWGRRU+HZOHWW3DFNDUGHUNHQGHVHUYLFHGLHQVW (UZRUGWJHHQDQGHUHVSHFLDOHJDUDQWLHYHUVWUHNW5HSDUDWLHRIYHUYDQJLQJ YDQHHQSURGXFWLVXLWVOXLWHQGXZHLJHQYHUDQWZRRUGHOLMNKHLG$OOH DQGHUHJHwPSOLFHHUGHJDUDQWLHVEHWUHIIHQGHYHUNRRSEDDUKHLGHQ FRQGLWLHYDQKHWDSSDUDDWJHOGHQXLWVOXLWHQGYRRUGH JDUDQWLHSHULRGHYDQGLWVFKULIWHOLMNHEHZLMV'RRUGDWLQVRPPLJH ODQGHQEHSHUNLQJHQDDQJDDQGHGHGXXUYDQGHJHw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

Klantentransacties in het Verenigd Koninkrijk 'H]HJDUDQWLHLVQLHWYDQWRHSDVVLQJRSNODQWHQWUDQVDFWLHVHQKHHIWJHHQ LQYORHGRSGHJURQGZHWWHOLMNHUHFKWHQYDQHHQFRQVXPHQW0HW EHWUHNNLQJWRWGHUJHOLMNHWUDQVDFWLHVZRUGHQGHUHFKWHQHQYHUSOLFKWLQJHQ YDQNRSHUHQYHUNRSHUELMZHWEHSDDOG



Als de calculator service nodig heeft +HZOHWW3DFNDUGKHHIWVHUYLFHGLHQVWHQLQYHOHODQGHQ'H]HGLHQVWHQ UHSDUHUHQFDOFXODWRUVRIYHUYDQJHQGH]HGRRUKHW]HOIGHPRGHORIGRRU HHQPRGHOPHWHHQKRJHUHZDDUGHRQJHDFKWGHJDUDQWLHEHSDOLQJHQ1D KHWYHUVWULMNHQYDQGHJDUDQWLHSHULRGHZRUGHQYRRUVHUYLFHNRVWHQLQ UHNHQLQJJHEUDFKW*HZRRQOLMNJHVFKLHGWRQGHUKRXGDDQHQWHUXJ]HQGLQJ YDQFDOFXODWRUVELQQHQYLMIZHUNGDJHQ

Service-adressen n In de Verenigde Staten:6WXXUGHFDOFXODWRUQDDUHHQHUNHQGH+3

VHUYLFHGLHQVW]LHELQQHQ]LMGHRPVODJ n In Europa:1HHPFRQWDFWRSPHW+HZOHWW3DFNDUGLQ1HGHUODQGRI %HOJLs]LHELQQHQ]LMGHRPVODJ KHW(XURSHVHKRRIGNZDUWLHUYDQ +HZOHWW3DFNDUGRIPHWXZGHDOHUYRRUDGUHVVHQYDQGH GLFKWVWELM]LMQGHVHUYLFHGLHQVW9HUVWXXUGHFDOFXODWRUQLHWYRRURQGHUKRXG ]RQGHUHHUVWFRQWDFWRSJHQRPHQWHKHEEHQPHWHHQ+HZOHWW3DFNDUGYHVWLJLQJ *DQDDUKWWSZZZKSFRPFDOFXODWRUVYRRUHHQOLMVWYDQ VHUYLFHGLHQVWHQLQ(XURSD n In andere landen:1HHPFRQWDFWRSPHWKHW+HZOHWW3DFNDUG YHUNRRSNDQWRRURIPHWXZGHDOHURIVFKULMIQDDUHHQHUNHQGH+3 VHUYLFHGLHQVW]LHELQQHQ]LMGHRPVODJ YRRUDGUHVVHQYDQDQGHUH VHUYLFHGLHQVWHQ$OVSODDWVHOLMNJHHQVHUYLFHEHVFKLNEDDULVNXQWXGH FDOFXODWRUYRRUUHSDUDWLHVYHUVWXUHQQDDUHHQHUNHQGH+3 VHUYLFHGLHQVW 9HU]HQGLQJUHJHOLQJYDQKHULPSRUWHQGRXDQHNRVWHQ]LMQXZHLJHQ YHUDQWZRRUGHOLMNKHLG

Servicekosten 9RRUVHUYLFHYHUOHQLQJEXLWHQGHJDUDQWLHWHUPLMQEHVWDDQYDVWHWDULHYHQ +HWVHUYLFHFHQWUXP]LHELQQHQ]LMGHDFKWHUEODG NDQXYHUWHOOHQZDWGH NRVWHQ]LMQ'H]HNRVWHQ]LMQRQGHUKHYLJDDQGHSODDWVHOLMNHEHSDOLQJHQ YRRUYHUNRRSVEHODVWLQJHQ%7:DOVGH]HYDQWRHSDVVLQJ]LMQ 'HYDVWHUHSDUDWLHNRVWHQ]LMQQLHWYDQWRHSDVVLQJDOVGHFDOFXODWRUGRRU RQJHYDORIRQGHVNXQGLJJHEUXLNLVEHVFKDGLJG,QGH]HJHYDOOHQZRUGW KHWWDULHIEHSDDOGRSJURQGYDQEHVWHGHWLMGHQNRVWHQYRRUPDWHULDDO 130 A: Hulp, Batterijen en Service


Verzendinstructies $OVRQGHUKRXGQRGLJLV]HQGWXGHFDOFXODWRUQDDUGHGLFKWVWELM]LMQGH HUNHQGHVHUYLFHGLHQVWRIHHQHUNHQGLQ]DPHOSXQW n 9HUPHOGXZDGUHVHQYRHJHHQEHVFKULMYLQJYDQKHWSUREOHHPELM n $OVGHJDUDQWLHSHULRGHQRJQLHWLVYHUVWUHNHQGLHQWXHHQ DDQNRRSEHZLMVPHWYHUPHOGLQJYDQGHDDQNRRSGDWXPELMWHVOXLWHQ n 9RHJHHQLQNRRSRUGHUFKHTXHRIKHWQXPPHUYDQXZFUHGLWFDUG PHWJHOGLJKHLGVGXXU9,6$RI0DVWHU&DUG ELMRPGHVWDQGDDUG UHSDUDWLHNRVWHQPHHWHYROGRHQ /HWRS+HWLVPRJHOLMNGDWFUHGLWFDUGVQLHWDDQYDDUGZRUGHQLQ (XURSD0HHULQIRUPDWLHYLQGWXRSKWWSZZZKSFRP FDOFXODWRUV n 9HU]HQGGHFDOFXODWRUWHUYHUPLMGLQJYDQVFKDGHJRHGYHUSDNWLQ EHVFKHUPHQGYHUSDNNLQJVPDWHULDDO'HUJHOLMNHVFKDGHLVQLHWGRRU GHJDUDQWLHJHGHNWKHWLVGDDURPYHUVWDQGLJGHYHU]HQGLQJWH YHU]HNHUHQ n 9ROGRHGHYHU]HQGNRVWHQRQJHDFKWRIGHFDOFXODWRURQGHUJDUDQWLH YDOWRIQLHW

Garantie op service 8KHEWJDUDQWLHRSYHUOHHQGHVHUYLFHYRRUPDWHULDDOGHIHFWHQHQ RQWRHUHLNHQGYDNPDQVFKDSJHGXUHQGHQDVHUYLFHYHUOHQLQJRIYRRUGH UHVWYDQXZRRUVSURQNHOLMNHJDUDQWLHODQJVWHSHULRGHJHOGW

Servicecontracten ,QGH96LVHHQVHUYLFHFRQWUDFWEHVFKLNEDDUYRRUUHSDUDWLHHQ RQGHUKRXG=LHKHWIRUPXOLHUYRRULQGHKDQGOHLGLQJ9RRUPHHU LQIRUPDWLHNXQWXFRQWDFWRSQHPHQPHWHHQ+3VHUYLFHGLHQVW]LH ELQQHQ]LMGHRPVODJ



Verdere informatie V.S. 'LWWRHVWHOYROGRHWDDQ3DUWYDQGH)&&5XOHV*HEUXLNLV RQGHUKHYLJDDQYROJHQGHWZHHYRRUZDDUGHQ 'LWWRHVWHOPDJJHHQ VFKDGHOLMNHLQWHUIHUHQWLHYHURRU]DNHQHQ GLWWRHVWHOPRHWLQWHUIHUHQWLH NXQQHQRSYDQJHQRRNGHLQWHUIHUHQWLHGLHRQJHZHQVWHJHYROJHQNDQ KHEEHQ

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n 'HDQWHQQHRSQLHXZLQVWHOOHQ n 'HFDOFXODWRUHHQDQGHUHSODDWVJHYHQWHQRS]LFKWHYDQGH RQWYDQJVWDSSDUDWXXU ,QJHYROJH3DUWYDQGH)&&UHJHOVNXQQHQZLM]LJLQJHQRI DDQSDVVLQJHQDDQGH]HDSSDUDWXXUGLHQLHWXLWGUXNNHOLMNJRHGJHNHXUG]LMQ GRRU+HZOHWW3DFNDUGOHLGHQWRWKHWYHUYDOOHQYDQGHUHFKWHQYDQGH JHEUXLNHUWRWKHWJHEUXLNHQYDQGH]HDSSDUDWXXU Canada 7KLV&ODVV%GLJLWDODSSDUDWXVFRPSOLHVZLWK&DQDGLDQ(0&

&ODVV%UHTXLUHPHQWV

&HWDSSDUHLOQXPpULTXHGHODFODVVH%HVWFRPIRUPHjODFODVVH%GHV QRUPHVFDQDGLHQQHVGHFRPSDWLELOLWppOHFWURPDJQpWLTXHV&(0



Japan

Nederland

%DWWHULHVDUHGHOLYHUHGZLWKWKLVSURGXFW:KHQHPSW\GR QRWWKURZWKHPDZD\EXWFROOHFWWKHPDVVPDOOFKHPLFDO ZDVWH %LMGLWSURGXFW]LMQEDWWHULMHQJHOHYHUG:DQQHHUGH]HOHHJ ]LMQPRHWX]HQLHWZHJJRRLHQPDDULQOHYHUHQDOVNOHLQ FKHPLVFKDIYDO

Termen en condities voor de eindgebruiker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wQVWDOOHHUGHQ JHEUXLNWZRUGW$OV+3WLMGHQVGHJDUDQWLHSHULRGHRSGHKRRJWH ZRUGWJHVWHOGYDQGHUJHOLMNHGHIHFWHQGDQ]DO+3GHVRIWZDUHPHGLD ZDDUYDQGHSURJUDPPHHULQVWUXFWLHVQLHWZRUGHQXLWJHYRHUGDOV JHYROJYDQGHUJHOLMNHGHIHFWHQYHUYDQJHQ +3JDUDQGHHUWQLHWGDWGHZHUNLQJYDQ+3SURGXFWHQ RQRQGHUEURNHQRIIRXWYULM]DO]LMQ$OV+3QLHWLQVWDDWLVRPHHQ A: Hulp, Batterijen en Service 133


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sHQ1LHXZ=HHODQGGH JDUDQWLHWHUPHQXLWGH]HYHUNODULQJVOXLWHQEHKDOYHLQGHPDWHGLH GRRUGHZHWJHYLQJWRHJHVWDDQLVGHYHUSOLFKWHJURQGUHFKWHQGLHYDQ WRHSDVVLQJ]LMQRSGHYHUNRRSYDQGLWSURGXFWDDQXQLHWXLW EHSHUNHQRIZLM]LJHQGH]HQLHWHQ]LMQHUHHQDDQYXOOLQJRS



B Nog meer berekeningen IRR/YR Berekeningen 'HFDOFXODWRUEHSDDOW,55<5YRRUHHQYHU]DPHOLQJYDQFDVKIORZVPHW EHKXOSYDQZLVNXQGLJHIRUPXOHVGLHGHRSORVVLQJEHUHNHQHQ'H]HZRUGW JHYRQGHQGRRUHHQEHQDGHULQJYDQGHRSORVVLQJWHJHYHQHQYHUYROJHQV GH]HEHQDGHULQJWHJHEUXLNHQRPHHQDQGHUHEHUHNHQLQJXLWWHYRHUHQ 'LWZRUGWKHWLWHUHUHQGHSURFHVJHQRHPG ,QGHPHHVWHJHYDOOHQYLQGWGHFDOFXODWRUKHWJHZHQVWHDQWZRRUGRPGDW HUYDDNVOHFKWVppQRSORVVLQJLVYRRUGHEHUHNHQLQJ+HWEHUHNHQHQYDQ ,55<5YRRUEHSDDOGHYHU]DPHOLQJHQYDQFDVKIORZVLVHFKWHU LQJHZLNNHOGHU(UNXQQHQPHHUGDQppQRIJHHQ RSORVVLQJHQYRRUKHW SUREOHHP]LMQ,QGH]HJHYDOOHQWRRQWGHFDOFXODWRUHHQPHOGLQJGLHX KHOSWELMKHWLQWHUSUHWHUHQYDQZDWHULVJHEHXUG

Mogelijke resultaten bij het berekenen van IRR/YR 'HPRJHOLMNHUHVXOWDWHQYDQHHQ,55<5EHUHNHQLQJ]LMQ n Geval 1.'HFDOFXODWRUWRRQWHHQSRVLWLHYHRSORVVLQJ'LWLVGHHQLJH SRVLWLHYHRSORVVLQJ(UNXQQHQHFKWHUppQRIPHHUQHJDWLHYH XLWNRPVWHQEHVWDDQ n Geval 2.'HFDOFXODWRUYLQGWHHQQHJDWLHYHRSORVVLQJPDDUHHQ HQNHOYRXGLJHSRVLWLHYHRSORVVLQJEHVWDDWRRN8]LHWPos Irr Also8 NULMJWGHQHJDWLHYHRSORVVLQJWH]LHQGRRURS WHGUXNNHQRPGH PHOGLQJWHZLVVHQ8YLQGWGHSRVLWLHYHRSORVVLQJGRRUHHQVFKDWWLQJ LQWHYRHUHQ=LH´(HQVFKDWWLQJLQYRHUHQYRRU,55<5µ KLHURQGHU (UNXQQHQRRNQRJH[WUDQHJDWLHYHXLWNRPVWHQ]LMQ n Geval 3.'HFDOFXODWRUWRRQWHHQQHJDWLHIDQWZRRUGHQJHHQ PHOGLQJ'LWLVGHHQLJHRSORVVLQJ

R

B: Nog meer berekeningen 135


n Geval 4.'HFDOFXODWRUWRRQWGHPHOGLQJNot Found'LWJHHIWDDQ

GDWGHEHUHNHQLQJ]HHULQJHZLNNHOGLV(UNDQPHHUGDQppQSRVLWLHYH RIQHJDWLHYHRSORVVLQJ]LMQRIHUNDQJHHQRSORVVLQJ]LMQ2PPHWGH EHUHNHQLQJYHUGHUWHJDDQPRHWXHHQEHQDGHULQJRSVODDQ]LH KLHURQGHU n Geval 5.'HFDOFXODWRUWRRQWGHPHOGLQJNo Solution(ULVJHHQ RSORVVLQJ'H]HVLWXDWLHNDQYRRUNRPHQDOVHUHHQIRXWLVJHPDDNW ELMYRRUEHHOGELMKHWLQYRHUHQYDQGHFDVKIORZV(HQYDDN YRRUNRPHQGHIRXWGLHGH]HPHOGLQJWRWUHVXOWDDWKHHIWLVKHW SODDWVHQYDQKHWYHUNHHUGHWHNHQYRRUHHQFDVKIORZ(HQFRUUHFWH VHULHFDVKIORZVYRRUHHQ,55<5EHUHNHQLQJPRHWWHQPLQVWHppQ SRVLWLHYHHQppQQHJDWLHYHFDVKIORZKHEEHQ

IRR/YR stoppen en opnieuw beginnen

R%

+HW]RHNHQQDDU,55<5NDQUHODWLHIODQJGXUHQ8NXQWGHEHUHNHQLQJ RSLHGHUPRPHQWVWRSSHQGRRURSGH WRHWVWHGUXNNHQ8]LHWGDQGH PHOGLQJIntErruPtEd$OVXQXRS GUXNW]LHWXGHEHQDGHULQJYDQ ,55<5YDQGLWRJHQEOLN8NXQWGHEHUHNHQLQJRSQLHXZODWHQEHJLQQHQ GRRUKHWYROJHQGHWHGRHQ n 'UXNRS WHUZLMOGHKXLGLJHEHQDGHULQJLQGHGLVSOD\ VWDDWZHHUJHJHYHQ+LHUGRRUZRUGWGHEHUHNHQLQJZHHUEHJRQQHQ YDQDIKHWSXQWZDDUGH]HZHUGDIJHEURNHQ n +HWRSVODDQYDQHHQVFKDWWLQJYRRU,55<5VWDDWKLHURQGHU EHVFKUHYHQ

*!*9

Een schatting invoeren voor IRR/YR

*!*9

8YRHUWHHQVFKDWWLQJLQGRRUHHQEHQDGHULQJYDQ,55<5LQWHYRHUHQ HQYHUYROJHQVRS WHGUXNNHQ8NXQWRSGHYROJHQGH PRPHQWHQHHQVFKDWWLQJYDQ,55<5LQYRHUHQ n 9yyUGHEHUHNHQLQJ(HQUHGHOLMNQDXZNHXULJHVFKDWWLQJNDQGH EHQRGLJGHWLMGYRRUKHWEHUHNHQHQYDQHHQRSORVVLQJYHUNRUWHQHQ GHNDQVGDWGHFDOFXODWRUHHQRQJHZHQVWHQHJDWLHYHRSORVVLQJYLQGW YHUPLQGHUHQ n 1DGDWXGHEHUHNHQLQJKHEWRQGHUEURNHQ n 1DGDWGHFDOFXODWRULVJHVWRSWGRRUppQYDQGHKLHUYRRUJHQRHPGH UHGHQHQ9RRUGHJHYDOOHQHQ]XOOHQHFKWHUJHHQDQGHUH RSORVVLQJHQZRUGHQJHYRQGHQ

136 B: Nog meer berekeningen


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

Gevolgen van het gebruik van Σ– voor het verbeteren van gegevens 'H+3%,,VODDWVWDWLVWLVFKHJHWDOOHQRS´JHDFFXPXOHHUGHµZLM]HRS 1LHWLHGHUJHWDOGDWXLQYRHUWZRUGWRSJHVODJHQPDDUHUZRUGHQ WXVVHQWLMGVHEHUHNHQLQJHQXLWJHYRHUGDOVXRSGH WRHWVGUXNW'H WRHWVYRHUWGHWHJHQRYHUJHVWHOGHEHUHNHQLQJHQXLWRPHHQJHWDORI HHQJHWDOOHQSDDUZHUNHOLMNWHYHUZLMGHUHQXLWGHRSJHVODJHQUHVXOWDWHQ

A

*@

%LMKHWYHUEHWHUHQYDQVWDWLVWLVFKHJHJHYHQVZRUGHQDIURQGLQJVIRXWHQ GLHELMWXVVHQWLMGVHEHUHNHQLQJHQYRRUNRPHQWLMGHQVEHZHUNLQJHQGLHPHW ]LMQXLWJHYRHUGQLHWGRRU YHUZLMGHUG+LHUGRRUNXQQHQ UHVXOWDWHQYRRUYHUEHWHUGHJHJHYHQVDIZLMNHQYDQJHJHYHQVGLHLQJHYRHUG ]LMQ]RQGHUGDW JHEUXLNWZHUG+HWYHUVFKLOLVHFKWHUQLHWYDQ EHODQJWHQ]LMGHRQMXLVWHJHJHYHQV]HHUJURRW]LMQWHQRS]LFKWHYDQGH MXLVWHJHJHYHQVLQGLWJHYDOLVKHWZDDUVFKLMQOLMNEHWHURPVWDWLVWLVFKH UHJLVWHUVWHZLVVHQHQGHJHJHYHQVRSQLHXZLQWHYRHUHQ

A

*@

*@

Getallenbereik 'HJURRWVWHSRVLWLHYHHQQHJDWLHYHJHWDOOHQZDDUPHHGHFDOFXODWRUZHUNW ]LMQïGHNOHLQVWHSRVLWLHYHHQQHJDWLHYHJHWDOOHQ ]LMQï²(HQXQGHUIORZJHHIWNRUWUFLOZHHUJHYROJGGRRUQXO 5DDGSOHHJGHPHOGLQJHQOFLOHQUFLOLQ´0HOGLQJHQµLQKHW KLHUQDYROJHQGHDDQKDQJVHO



Formules Berekening van marge en brutowinst 35& – .267 0$5 =   ×   35&

35& – .267 08 =   ×  .267 

Time Value of Money (TVM) %HWDOLQJVPRGXVIDFWRU6 YRRUGH(LQGPRGXVYRRUGH%HJLQPRGXV ,<5 L = 3<5 L    –     × S × 307 × ------------------------------------- 0 = PV +  + L --------------   L    -------  –N

L + FV ×  1 + --------  


–N


Amortisatie Σ,17

JHFXPXOHHUGHUHQWH

Σ351

JHFXPXOHHUGHKRRIGVRP

L

SHULRGLHNHUHQWHYRHW

%$/LVLQHHUVWHLQVWDQWLHJHOLMNDDQ39DIJHURQGQDDUGHKXLGLJH LQVWHOOLQJYDQGHGLVSOD\ 307LVLQHHUVWHLQVWDQWLHJHOLMNDDQ307DIJHURQGQDDUGHKXLGLJH LQVWHOOLQJYDQGHGLVSOD\ ,<5 i = ----------------------------3 ⁄ <5 × 9RRULHGHUHJHDPRUWLVHHUGHDIEHWDOLQJ ,17

%$/ïL,17·ZRUGWDIJHURQGQDDUGHKXLGLJHLQVWHOOLQJ YDQGHGLVSOD\,17· YRRUSHULRGHLQGH%HJLQPRGXV

,17

,17 PHWKHWWHNHQYDQ307

351

307,17

%$/QLHXZ

%$/RXG351

Σ,17QLHXZ

Σ,17RXG,17

Σ351QLHXZ

Σ351RXG351

Rentevoet conversies 120 P ⁄ YR  – × ()) =   1 + -----------------------------   × 3 ⁄ <5



Cashflowberekeningen L M &)M

SHULRGLHNHUHQWHYRHW KHWQXPPHUYDQGHFDVKIORZJURHS KHWEHGUDJYDQGHFDVKIORZYRRUJURHSM

QM

DDQWDONHUHQGDWGHFDVKIORZYRRUNRPWYRRUJURHSM

N

KHWQXPPHUYDQGHODDWVWHJURHSYDQFDVKIORZV

1M

∑ n l WRWDDODDQWDOFDVKIORZVYRRUDIJDDQGDDQGHJURHSM

1≤l<j

L  j  1 –  1 + ------k      L –nj NPV = CF 0 + ∑ CF j ×  ------------------------------------- × 1 + -------- L     -------j=1   –n

$OV139 LVGHRSORVVLQJYRRULKHWSHULRGLHNHLQWHUQHUHQGHPHQW



Statistiek ∑ [\ ∑[ ∑y [ = ------- y = ------- [ Z = ---------Q Q ∑\ 2

Sx =

(∑ [) ∑ [ – -------------Q ------------------------------Q– 2

Sy =

(∑ y) ∑ y – -------------Q -----------------------------Q– 2

(∑ [) ∑ [ – -------------Q ------------------------------- σy = Q

σx =

2

(∑ y) ∑ y – -------------Q ------------------------------ Q

∑ x∑ y ∑ xy – --------------n r = ---------------------------------------------------------------------------2 2 (∑ x)   2 (∑ y)   ∑ x 2 – ------------- ∑ y – ------------- n  n  ∑ x∑ y ∑ xy – --------------n m = -------------------------------2(∑ x) 2 ∑ x – -------------n y–b b = y – mx xˆ = ----------- yˆ = mx + b m




C Meldingen

%RIRRPHHQPHOGLQJYDQGHGLVSOD\WHZLVVHQ

'UXNRS All Clear

+HWEOLMYHQGJHKHXJHQLVJHZLVWSDJLQD COPR HP2000

&RS\ULJKWEHULFKW Interrupted

(HQ,55<5,<5RIDPRUWLVDWLHEHUHNHQLQJZHUGRQGHUEURNHQGRRU KHWLQGUXNNHQYDQ

%

No Solution

*HHQ2SORVVLQJ (UEHVWDDWJHHQRSORVVLQJYRRUGHLQJHYRHUGH ZDDUGHQSDJLQD Not Found

(UNDQHHQRSORVVLQJEHVWDDQYRRU,55<5RI,<5$OVXSUREHHUWRP ,<5RSWHORVVHQLVKHWPRJHOLMNGDWXGHEHUHNHQLQJNXQWXLWYRHUHQPHW JHEUXLNYDQ,55<5$OVXHHQ,55<5EHUHNHQLQJSUREHHUWRSWH ORVVHQ]LHGDQSDJLQD OFLO

2YHUIORZ +HWUHVXOWDDWYDQHHQEHUHNHQLQJLVWHJURRWYRRUGH FDOFXODWRURPPHHWHNXQQHQZHUNHQ'HPHOGLQJZRUGWJHGXUHQGHHHQ NRUWPRPHQWJHWRRQGHQYHUYROJHQV]LHWXKHWUHVXOWDDWYDQGHRYHUIORZ ( 'HRYHUIORZPHOGLQJ]LHWXRRNDOVKHWUHVXOWDDW YDQHHQWXVVHQWLMGVH790RIFDVKIORZEHZHUNLQJHHQRYHUIORZVLWXDWLHWRW JHYROJKHHIW,QGLWJHYDOEOLMIWGHPHOGLQJLQGHGLVSOD\VWDDQ

C: Meldingen 143


Pos Irr Also

3RVLWLYH,QWHUQDO5DWHRI5HWXUQ$OVR2RNHHQSRVLWLHYHLQWHUQH UHQWHYRHW (HQEHUHNHQLQJYDQ,55<5KHHIWHHQQHJDWLHYHRSORVVLQJ (UEHVWDDWRRNHHQSRVLWLHYHRSORVVLQJSDJLQD Running

5XQQLQJ%H]LJ (UZRUGWHHQEHUHNHQLQJXLWJHYRHUG UFLO

8QGHUIORZ (HQWXVVHQWLMGVUHVXOWDDWLQ790LVWHNOHLQYRRUGH+3 %,,RPPHHWHNXQQHQZHUNHQ'LWEHULFKWZRUGWRRNNRUW ZHHUJHJHYHQDOVHUXQGHUIORZRSWUHHGWELMHHQEHZHUNLQJ,QGDWJHYDO ZRUGWKHWJHYROJGGRRUQXO

144 C: Meldingen


Index 7RHWVHQGLHKLHUQLHWZHHUJHJHYHQ]LMQ NXQWXWHUXJYLQGHQLQGHDOIDEHWLVFKH VHFWLHVYDQGH]HLQGH[

"d T[ ( )* R U 6M ;= \g A@ f$ E3 4

Speciale tekens , , ,

A $DQ]HWWHQ $IURQGHQ $IZLMNHQGHHHUVWHEHWDOLQJ AMORT $PRUWLVDWLH – HQNHOYRXGLJHEHWDOLQJ , IRUPXOHV KRRIGVRP UHHNVYDQEHWDOLQJHQ UHQWH VDOGR $PRUWLVDWLHLQppQRRJRSVODJ $QQXwWHLW $35

B %DFNVSDFH BAL %DOORQEHWDOLQJ , %DVLVLGHHsQLQppQRRJRSVODJ %DWWHULHV %DWWHULMHQ ELMQDOHHJ SODDWVHQ BEGIN , %HJLQPRGXV %HQDGHULQJ ,

O

Index 145


%HWDOLQJ EDOORQ SHULRGHV YRRUXLW %UXWRZLQVW ,

2 %& C

&DVKIORZ &DVKIORZ EHNLMNHQ GLDJUDPPHQ HHUVWH IRUPXOHV LQYRHUHQ RQJHOLMN YHUGLVFRQWHUHQ YHUYDQJHQ YRRUEHHOGHQ YUDDJVWXNNHQ , – CF C - FLOW &LMIHUVVFKHLGLQJVWHNHQ &RQVWDQWHQ &RQWDQWHZDDUGH &RQWLQXHVDPHQVWHOOLQJYDQUHQWH &RUUHODWLHFRsIILFLsQW , &XUVRU

, j 7 D

'HFLPDOHQ 'LVSOD\KHOGHUKHLG 'LVSOD\IRUPDDW 'XL]HQGWDOOHQVFKHLGLQJVWHNHQ 146 Index

' Z E

(HUVWHFDVKIORZ (IIHFWLHYHUHQWH (LQGPRGXV (QNHOYRXGLJHUHQWH ERROR ([SRQHQWHQ

F )DFXOWHLW )RUPXOHV DPRUWLVDWLH FDVKIORZEHUHNHQLQJHQ PDUJHVHQEUXWRZLQVW UHQWHFRQYHUVLHV VWDWLVWLHN 790 )RXWPHOGLQJHQ FULL FUNC )XQFWLHV

/ G

*DUDQWLH *HKHXJHQ ZLVVHQ , *HKHXJHQWRHWVHQLQppQRRJ RSVODJ *HNDSLWDOLVHHUGHZDDUGH *HPLGGHOGH , , JHZRJHQ , *HWDOOHQ DIURQGHQ EHUHLNYDQ QHJDWLHI RSVODDQ YROOHGLJHQDXZNHXULJKHLG


*HWDOQRWDWLH GLVSOD\IRUPDDW *HZRJHQJHPLGGHOGH ,

H +DDNMHV +HOGHUKHLGYDQGHGLVSOD\ +RRIGVRP +\SRWKHNHQ PHWHHQEDOORQEHWDOLQJ YHUGLVFRQWHHUG YRRUEHHOGYDQ ZUDSDURXQG

I

0

,QGLFDWRUV INT ,QYHUVH ,55 EHUHNHQHQ ,55<5 , DXWRPDWLVFKHRSVODJYDQ LQppQRRJRSVODJ ,55<5EHUHNHQLQJHQ PRJHOLMNHUHVXOWDWHQ RSQLHXZEHJLQQHQ VFKDWWLQJHQLQYRHUHQ VWRSSHQ

.9 J

-DDUOLMNVSHUFHQWDJH -DDUOLMNVHHIIHFWLHYHUHQWH -DDUOLMNVHQRPLQDOHUHQWH -DDUOLMNVHRSEUHQJVW

K

.HWWLQJEHZHUNLQJHQ .RPPDDOVVFKHLGLQJVWHNHQ .RPPDVFKHLGLQJVWHNHQ .RUWHKDQGOHLGLQJ .RUWLQJ .RVWHQ .RVWHQLQGLHQQLHWFRQWDQW EHWDDOG .ZDGUDDW

L /HDVH PHWYRRUXLWEHWDOLQJHQ /HQLQJ]RQGHUWXVVHQWLMGVH DIORVVLQJ /HQLQJHQ , DDQWDOEHWDOLQJHQ DIZLMNHQGHHHUVWHSHULRGH ]RQGHUWXVVHQWLMGVHDIORVVLQJ /HQLQJHQRSEDVLVYDQYDVWJRH GHLJHQGRP /LQHDLUHUHJUHVVLH , /RJDULWPH

?

M

, 0DFKW 0DUJH , 0HOGLQJHQ , YHUZLMGHUHQ 0UHJLVWHU

Index 147


+P e N

N 1DWXXUOLMNORJDULWPH 1DXZNHXULJKHLG 1HJDWLHYHJHWDOOHQ 1HWWRWRHNRPVWLJHZDDUGH 1RPLQDOHUHQWH 139 DXWRPDWLVFKHRSVODJYDQ EHUHNHQHQ LQppQRRJRSVODJ

C N W 1 O

2PJHYLQJVIDFWRUHQ 2QJHOLMNHFDVKIORZ 2SHUDWRUHQUHNHQNXQGLJ 2SQLHXZLQVWHOOHQ 2SVODDQ

P 3HUFHQWDJH RSWHOOHQRIDIWUHNNHQ YHUDQGHULQJ 3HUFHQWDJHV 3HULRGHV , , , 3HULRGLHNHUHQWH 3RSXODWLHVWDQGDDUGGHYLDWLH 3ULMV , PRIN PEND PER

2 c

148 Index

3UREOHPHQRSORVVHQ 3URFHQW 3URFHQWHQ LQppQRRJRSVODJ 39=LH&RQWDQWHZDDUGH

b R

, 5HFLSURTXH 5HJLVWHUV JHQXPPHUG UHNHQNXQGLJHEHZHUNLQJHQLQ VWDWLVWLHN 5HJUHVVLH 5HNHQNXQGLJHEHZHUNLQJHQ 5HNHQNXQGLJHRSHUDWRUHQ 5HQGHPHQW 5HQWH HIIHFWLHYH , HQNHOYRXGLJH QRPLQDOH , SHULRGLHNH VDPHQJHVWHOGH 5HQWHYRHWFRQYHUVLHLQppQRRJ RSVODJ 5HQWHYRHWFRQYHUVLHV 5HVLGXZDDUGH , 5LFKWLQJVFRsIILFLsQW ,

aL S

6DOGRYDQGHOHQLQJ 6DPHQJHVWHOGHUHQWH 6DPHQVWHOOLQJVSHULRGHV HQEHWDOLQJVSHULRGHV YHUVFKLOOHQGHSHULRGHV 6FKDWWHQYDQ,55<5 6FKHLGLQJVWHNHQV


6HUYLFH (XURSD 86$ DQGHUHODQGHQ SHIFT 6KLIWWRHWV VQLMSXQWPHWGH\DV 6RPPDWLHVWDWLVWLHNHQ 6SDUHQ , 6WDQGDDUGGHYLDWLH , SRSXODWLH VWHHNSURHI STAT , 6WDWLVWLHN ppQYDULDEHOH JHJHYHQVLQYRHUHQ JHPLGGHOGH LQppQRRJRSVODJ UHJLVWHUV VWDQGDDUGGHYLDWLH WRHWV ZLVVHQ , , 6WDWLVWLHNHQ EHQDGHULQJ , JHPLGGHOGH OLQHDLUHUHJUHVVLH VRPPDWLH VWDQGDDUGGHYLDWLH WZHHYDULDEHOHQ YHUZDFKWLQJHQ 6WDWLVWLHNHQPHWppQYDULDEHOH 6WDWLVWLHNHQPHWWZHHYDULDEHOHQ 6WHHNSURHIVWDQGDDUGGHYLDWLH

:

!i

T 7HNHQYHUDQGHUHQ 7HUPHQHQFRQGLWLHV 7RHNRPVWLJHZDDUGH , 790 IRUPXOHV LQppQRRJRSVODJ – YUDDJVWXNNHQ TVM

U 8LWNRRSZDDUGH 8LWVWDDQGEHGUDJ 8LW]HWWHQ

V 9DVWJRHGHLJHQGRP 9HHOYRRUNRPHQGHYUDJHQ 9HUGHUHLQIRUPDWLH 9HUGLVFRQWHHUGHK\SRWKHNHQ 9HUGLVFRQWHUHQYDQFDVKIORZV 9HUNRRSSULMV 9HUNRRSSULMVYDVWVWHOOHQ 9HUYDOZDDUGH 9HUZDFKWLQJHQ , 9HUZLMGHUHQ PHOGLQJHQ 9LHUNDQWVZRUWHO 9RRUXLWEHWDOLQJ 9RRUXLWEHWDOLQJHQ 9RRUZDDUGHQELMJHEUXLN 9UDJHQ

Index 149


W :HWHQVFKDSSHOLMNHQRWDWLH :LVVHQ GLVSOD\ JHKHXJHQ VWDWLVWLHNHQ 790 :RUWHOV

150 Index

:UDSDURXQGK\SRWKHNHQ

h ^ X

Y

hp 10BII Zakelijke Calculator

Recommend Documents