日期:2012/10/10

何謂年金終值? 年金終值是指年金終值從第一期起一定時期內每期期末等額收付款項的複利終值之和,或者說是在一個固定利率下定期定額投資數期之後的本金和。為了快速計算年金終值在若干年後的利率,可以直接透過年金終值表查表得知喔…

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年金終值計算公式:

已知複利終值公式p(1 + i)n, 所以可得每期定額 p在經過n期之後本利和F如下

 F = p+ p(1 + i)+p(1 + i)2+…+p(1 + i)n-1…..(1)式

再將(1)式乘上(1 + i)之後減去(1)式, 最後可得本利和F

F =p [(1 + i)n-1]/i

其中[(1 + i)n-1]/i 稱為年金終值係數,在實際運用時,通常查年金終值表得到其解,其中i為每期固定利率, n為期數, F為本利和,p為每期本金(定期定額)。

以下是年金終值表的算例:

小明每年定期定額存入10萬元 , 假設每年的投資報酬率為10%, 請問5年後可領回多少本利和?

本利和F=100000× [(1 + i)n-1]/i=100000×[(1.1)5-1]/0.1=100000×年金終值係數(可直接查閱年金終值表)=100000×6.1051=610510元

年金終值表如下表所示,

期數n 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100
3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310
4 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641
5 5.101 5.204 5.309 5.416 5.526 5.637 5.751 5.867 5.985 6.105
6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716
7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487
8 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.637 11.028 11.436
9 9.369 9.755 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579
10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937
11 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531
12 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384
13 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523
14 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975
15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772
16 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950
17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33.750 36.974 40.545
18 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599
19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159
20 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275
21 23.239 25.783 28.676 31.969 35.719 39.993 44.865 50.423 56.765 64.002
22 24.472 27.299 30.537 34.248 38.505 43.392 49.006 55.457 62.873 71.403
23 25.716 28.845 32.453 36.618 41.430 46.996 53.436 60.893 69.532 79.543
24 26.973 30.422 34.426 39.083 44.502 50.816 58.177 66.765 76.790 88.497
25 28.243 32.030 36.459 41.646 47.727 54.865 63.249 73.106 84.701 98.347
26 29.526 33.671 38.553 44.312 51.113 59.156 68.676 79.954 93.324 109.182
27 30.821 35.344 40.710 47.084 54.669 63.706 74.484 87.351 102.723 121.100
28 32.129 37.051 42.931 49.968 58.403 68.528 80.698 95.339 112.968 134.210
29 33.450 38.792 45.219 52.966 62.323 73.640 87.347 103.966 124.135 148.631
30 34.785 40.568 47.575 56.085 66.439 79.058 94.461 113.283 136.308 164.494

希望這篇文章能夠讓大家受用^^


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