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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