Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
Uitwerkingen opgaven
hoofdstuk 7
7.1 a
1
⎛
⎜ 1 − (1, 065)15
RW= 0,06 × 250.000 × ⎜
0, 065
⎜
⎜
⎝
⎞
⎟
1
⎟ + 250.000 ×
(1, 065)15
⎟
⎟
⎠
RW= 15.000 × a15|6,5 + 250.000 × A15|6,5 =238.246,66
b
1
⎛
⎜ 1 − (1, 065)4
RW= 0,06 × 250.000 × ⎜
0, 065
⎜
⎜
⎝
⎞
⎟
1
⎟ + 250.000 ×
(1, 065)4
⎟
⎟
⎠
RW= 15.000 × a4|6,5 + 250.000 × A4|6,5 =245.717,75
⎛
⎞
1
1
1
1
Ca = 8.000 × ⎜
×
=
+
+ ... +
1
2
5 ⎟
1, 085
(1, 08)
(1, 08) ⎠
⎝ (1, 08)
7.5
1
1−
8.000 ×
5
1, 08
0, 08
×
RW = 21.738,97 +
7.6 a
= 8.000 × a5|8 × A5|8 = 21.738,97
6
× (40.000 − 21.738,97) = 35.434,74
8
⎛
⎞
1
1
1
1
Ca = 10.000 × ⎜
×
=
+
+ ... +
1
2
10 ⎟
1, 073
(1, 07)
(1, 07) ⎠
⎝ (1, 07)
1−
10.000 ×
1
10
1, 07
0, 07
RW = 57.333,35 +
1−
b
1
1, 085
Ca = 10.000 ×
1
×
1, 073
8
× (100.000 − 57.333,35) = 106.095,24
7
1
10
1, 07
0, 07
RW = 70.235,82 +
= 10.000 × a10|7 × A3|7 = 57.333,35
= 10.000 × a10|7 = 70.235,82
8
× (100.000 − 70.235,82) = 104.252,03
7
Uitwerkingen opgaven hoofdstuk 7 | 1
Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
1
1−
c
1, 07
0, 07
Ca = 10.000 ×
RW = 33.872,11 +
4
= 10.000 × a4|7 = 33.872,11
8
× (40.000 − 33.872,11) = 40.875,41
7
0, 07 × 75.000 = 5.250
= 65.625
0, 08
7.8
RW =
7.9
Waarde:
7.11 a
18.000
= 150.000
0,12
1
Ann = 275.000 ×
1
1−
(1, 07)20
0, 07
20
1, 08
0, 08
RW = 25.958,05 ×
RW = 254.859,96 = Ca +
254.859,96 =
= 275.000 ×
1
= 25.958,05
a20|7
1
1−
b
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
= 25.958,05 × a20|8 = 254.859,96
7
× (275.000 − Ca )
8
1
× Ca + 240.625
8
Ca = 113.879,68
c
Ci = RW − Ca = 140.980,28
1−
7.12 a
Ca = 10.000 ×
30
1, 06
0, 06
RW = 137.648,31 +
RK =
1
= 10.000 × a30|6 = 137.648,31
8
× (300.000 − 137.648,31) = 354.117,23
6
354.117,23
× 100% = 118,0%
300.000
Uitwerkingen opgaven hoofdstuk 7 | 2
Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
1
1−
b
20
1, 06
0, 06
Ca = 10.000 ×
RW = 114.699,21 +
= 10.000 × a20|6 = 114.699,21
8
× (200.000 – 114.699,21) = 228.433,60
6
228.433,60
× 100% = 114,2%
200.000
RK =
c
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
Ca = 10.000 ×
1
= 10.000 × A1|6 = 9.433,96
1, 06
RW = 9.433,96 +
8
× (10.000 − 9.433,96) = 10.188,68
6
RK =
10.188,68
× 100% = 101,9%
10.000
7.13
RK =
142.385, 69
× 100% = 96%
148.194,54
7.14
RK =
p
× 100% = 80%
5
p = 4%
7.16
⎛
⎞
1
1
1
1
Ca = 5.000 × ⎜
×
=
+
+ ... +
1
2
15 ⎟
1, 085
(1, 08)
(1, 08) ⎠
⎝ (1, 08)
1−
5.000 ×
Ci =
1
15
1, 08
0, 08
×
1
1, 085
= 5.000 × a15|8 × A5|8 = 29.127,19
7
⎛1
⎞
× (75.000 − 29.127,19) × ⎜ × (1, 080,5 + 1) ⎟ = 40.926,04
8
⎝2
⎠
RW = 29.127,19 + 40.926,03 = 70.053,23
7.17
Ca = 360.000 ×
Ci =
1
= 360.000 × A10|10 = 138.795,58
1,1010
9
× (360.000 − 138.795,58) = 199.083,98
10
RW = 138.795,58 + 199.083,98 = 337.879,56
Uitwerkingen opgaven hoofdstuk 7 | 3
Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
C p = 360.000 − 337.879,56 = 22.120,44
1
= premie × A10|10
1,1010
22.120,44 = premie ×
Premie = 57.374,72 ofwel 15,9% van 360.000
1−
7.19
1
10
1, 05
0, 05
Agio = (0,08 – 0,05) × 100.000 ×
= 3.000 × a10|5 = 23.165,20
Of:
Agio = RW – 100.000
1−
RW = 0,08 × 100.000 ×
1
10
1, 05
0, 05
+ 100.000 ×
1
=
1, 0510
8.000 × a10|5 + 100.000 × A10|5 = 123.165,20
Agio = 123.165,20 – 100.000 = 23.165,20
1−
7.20 a
Ca = 20.000 ×
RW = 213.495,52 +
1−
b
Ca = 20.000 ×
1−
Ca = 30.000 ×
25
= 20.000 × a25|8 = 213.495,52
7
× (500.000 − 213.495,52) = 464.186,94
8
1
15
1, 08
0, 08
RW = 171.189,57 +
7.21
1
1, 08
0, 08
= 20.000 × a15|8 = 171.189,57
7
× (300.000 − 171.189,57) = 283.898,69
8
1
5
1, 055
0, 055
1−
+ 50.000 ×
1
3
1, 055
0, 055
×
1
1, 0555
=
30.000 × a5|5,5 + 50.000 × a3|5,5 × A5|5,5 = 231.322,61
RW = 231.322,61 +
5
× (300.000 − 231.322,61) = 293.756,60
5,5
Uitwerkingen opgaven hoofdstuk 7 | 4
Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
7.22
RW =
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
0, 05 × 1.000 = 50
= 666,67
r
r = 0,074999 ofwel p’ = 7,5%
1
Ann = 450.000 ×
7.23
1
1−
(1, 075)30
0, 075
1−
Ca = 10.000 ×
10
1,10
0,10
RW = 41.968,22 +
RK =
10
= 10.000 × a10|10 x A4|10 = 41.968,22
= 10.000 × a10|10 = 61.445,67
9
× (100.000 − 61.445,67)= 96.144,57
10
1
Ca = 10.000 ×
5
1,10
0,10
RW = 37.907,87 +
c
1,104
96.144,57
× 100% = 96,1%
100.000
1−
RK =
1
1
1,10
0,10
RW = 61.445,67 +
c
×
94.196, 82
× 100% = 94,2%
100.000
Ca = 10.000 ×
RK =
= 38.102,06 × a30|8 = 428.944,74
9
× (100.000 − 41.968,22) = 94.196,82
10
1−
b
30
1
1−
7.24 a
1
= 38.102,06
a30|7,5
1
1, 08
0, 08
RW = 38.102,06 ×
= 450.000 ×
= 10.000 × a5|10 = 37.907,87
9
× (50.000 − 37.907,87) = 48.790,79
10
48.790,79
× 100% = 97,6%
50.000
Ca = 10.000 ×
1
1,10
= 10.000 × A1|10 = 9.090,91
Uitwerkingen opgaven hoofdstuk 7 | 5
Auteur: Gruijters
www.financielerekenkunde.noordhoff.nl
RW = 9.090,91 +
RK =
9
× (10.000 − 9.090,91) = 9.909,09
10
9.909, 09
× 100% = 99,1%
10.000
1
1−
7.25 a
Ca = 6.000 ×
Ci =
isbn: 978-90-01-80952-2
© 2012 Noordhoff Uitgevers bv
10
1, 055
0, 055
=6.000 × a10|5,5 = 45.225,75
5
⎛1
⎞
× (60.000 − 45.225,75) × ⎜ × (1, 0550,5 + 1) ⎟ = 13.613,34
5,5
⎝2
⎠
RW = 45.225,75 + 13.613,34 = 58.839,09
RK =
b
58.839, 09
× 100% = 98,1%
60.000
Ca = 6.000 ×
Ci =
1
1, 055
= 6.000 × A1|5,5 = 5.687,20
5
⎛1
⎞
× (6.000 − 5.687,20) × ⎜ × (1, 0550,5 + 1) ⎟ = 288,22
5,5
2
⎝
⎠
RW = 5.687,20 + 288,22 = 5.975,42
RK =
5.975, 42
× 100% = 99,6%
6.000
1−
7.26
Ca = 8.000 ×
Ci =
1
15
1, 06
0, 06
=8.000 × a15|6 = 77.697,99
4,5
× (120.000 − 77.697,99) = 31.726,51
6
C p = 0,005 × 77.697,99 = 388,49
RW inclusief aflossingspremie = 77.697,99 + 31.726,51 + 388,49 =
109.812,99
Uitwerkingen opgaven hoofdstuk 7 | 6

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