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Samenvatting Financiële algebra
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Samenvatting van 76 pagina's voor het vak Financiële algebra aan de Artesis (Examen: 17/20.)
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Financiëlealgebra
Samenvatting: Financiële
algebra
2022-2023
1AF
Lector B.
,Inhoudsopgave
1. Inleiding ............................................................................................................................................. 4
Basis...................................................................................................................................................................... 4
2. Enkelvoudige intrest ........................................................................................................................... 5
Symbolen .............................................................................................................................................................. 5
Formules ............................................................................................................................................................... 5
Oefeningen ........................................................................................................................................................... 5
3. Handelsdisconto – enkelvoudig disconto ........................................................................................... 10
Symbolen ............................................................................................................................................................ 10
Formules ............................................................................................................................................................. 10
4. Samengestelde intrest ...................................................................................................................... 11
Symbolen ............................................................................................................................................................ 11
Formules ............................................................................................................................................................. 11
Oefeningen ......................................................................................................................................................... 12
Digitap ................................................................................................................................................................ 17
5. Gelijkwaardige rentevoeten .............................................................................................................. 18
Formules ............................................................................................................................................................. 18
Oefeningen ......................................................................................................................................................... 18
6. Bepaalde vervaldag, gemiddelde vervaldag ....................................................................................... 19
Symbolen ............................................................................................................................................................ 19
Digitap ................................................................................................................................................................ 19
7. Samengesteld disconto ..................................................................................................................... 23
Symbolen ............................................................................................................................................................ 23
Formules ............................................................................................................................................................. 23
Oefeningen ......................................................................................................................................................... 23
8. Annuïteiten ...................................................................................................................................... 26
Basis.................................................................................................................................................................... 26
Symbolen ............................................................................................................................................................ 28
Formules ............................................................................................................................................................. 28
Oefeningen (annuïteiten) ................................................................................................................................... 30
Digitap ................................................................................................................................................................ 34
2
, Oefeningen (termijnen) ...................................................................................................................................... 36
Extra ................................................................................................................................................................... 38
9. Gemiddelde vervaldag ...................................................................................................................... 39
Symbolen ............................................................................................................................................................ 39
Formules ............................................................................................................................................................. 39
Oefeningen ......................................................................................................................................................... 39
10. Annuïteitenlening......................................................................................................................... 40
Formule............................................................................................................................................................... 40
Oefeningen ......................................................................................................................................................... 40
11. Lening met reconstitutie (of wedersamenstelling) ......................................................................... 45
Formule............................................................................................................................................................... 45
Oefening ............................................................................................................................................................. 45
12. Extra ............................................................................................................................................ 47
Notities ............................................................................................................................................................... 47
Excel.................................................................................................................................................................... 62
3
,1. Inleiding
Basis
Contract in bepaalde periode = altijd in jaar uitgedrukt:
• 6 maanden = 1 semester = 1/2 jaar
• 3 maanden = 1 trimester of kwartaal = 1/4 jaar
• 1 maand = 1/12 jaar
% = alleen in vraagstukken/tekst = nooit in berekening zetten berekening:
• Peruun = perunage = % delen 100
• Bv. 25% = peruun = 0,25
4
,2. Enkelvoudige intrest
Symbolen
Kn of K = eindkapitaal
k = beginkapitaal (= vergrotende factor)
i = interestvoet of rentevoet of renteperuun (= altijd in %)
I = intrest- of rentebedrag (= altijd een bedrag)
n = duurtijd of periode
s = saldo of rest
Formules
K = k . (1 + i.n) of K = k + (i.n.k) → I = k.i.n
k = K / (1 + i.n)
i = (K - k) / (k.n)
n = (K - k) / (i.k)
Oefeningen
Bepaal het eindkapitaal dat ontstaat als men € 100.000 gedurende 5 jaar tegen een enkelvoudige
intrest van 6 % belegt.
Gegevens:
k = 100.000
i = 6%
n = 5 jaar
Gevraagd: K = ?
Oplossing:
K = k x (1 + i.n)
= 100.000 x (1 + 6% x 5)
= 130.000
5
,Een aankoop wordt afgesloten voor een bedrag van € 84.995 contant. Bij levering wordt slechts €
14.170 vereffend en het saldo zal betaald worden na 6 maanden mits een enkelvoudige intrest van
7 % per jaar. Welk bedrag zal in totaal uitgegeven worden?
Gegevens:
k = 84.995
V of voorschot = 14.170
i = 7%
n = 6m = 6/12 j
Gevraagd: K = ?, s (saldo) = ?
n
Oplossing:
K = V + s (1 + i.n)
= 14.170 + (84.995 - 14.170) x (1 + 0,07 x 6/12)
= 87.473,875
Hoe groot is een kapitaal dat na 5 jaar enkelvoudige intrest aangroeit tot € 177.045? Jaarlijkse
intrest 9 %.
Gegevens:
K = 177.045
i = 9%
n=5j
Gevraagd: k = ?
Oplossing:
K = k (1 + i.n)
k = K / (1 + i.n)
= 177.045 / (1 + 9% x 5)
= 122.100
6
, Hoe groot is een kapitaal dat na 4 maanden tegen 9 % per jaar enkelvoudige intrest aangroeit tot €
95.000?
Gegevens:
K = 95.000
i = 9%
n = 4m = 4/12
Gevraagd: k = ?
Oplossing:
K = k (1 + i.n)
k = K / (1 + i.n)
= 95.000 / (1 + 9% x 4/12)
= 92.233,01
Hoe groot is een kapitaal dat tegen 8 % per jaar enkelvoudige intrest na 3 jaar € 6.480 intrest
opbrengt?
Gegevens:
i = 8%
n=3j
I = 6.480
Gevraagd: k = ?
Oplossing:
K =k+I
I =K-k
K = k (1 + i.n)
I = k (1 + i.n) - k
I = k.i.n
k = I / (i.n)
= 6.480 / (8% x 3)
= 27.000
7
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