上次有聊到72法則,我們來看看複利與72法則。
我們可以看到下面的1元的複利終值表。
可以看到上面軸是利率,左邊是期數,假設為年。
1元如果利率1%,在單筆投資複利後,放了70年會成長到2元,
1元如果利率10%,在單筆投資複利後,放了7年多會成長到2元,
是不是和之前說到,如果利率小於6%其實用70法則,大於6%以上用76法則誤差會較小一點。
這個表我們可以看到,以一般投資能夠每年達到4~6%穩定成長就很棒,
我們來看看如果幫子女存一筆出國留學的基金,或是出社會後的買房頭期款,
可以怎麼來利用。
假設有一筆投資每年成長6%,我們在小孩出生的時候就幫他存進去,
那麼到了小孩讀完大學約22歲的時候,可以得到3.604,也就是小孩一出生存入1元的話,
到了小孩大學畢業,就可以得到3.604元,約3.6倍的金額,
利用72法則的話,就是72/6=12年翻倍,在小孩12歲時可以成長到2元,
如果2元要成長到4元的話,還要再12年,也就是24歲,但因為22歲畢業,
還差2年,所以只有3.6倍。
每期利率 期數(年) |
1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% |
1 | 1.010 | 1.020 | 1.030 | 1.040 | 1.050 | 1.060 | 1.070 | 1.080 | 1.090 | 1.100 |
2 | 1.020 | 1.040 | 1.061 | 1.082 | 1.103 | 1.124 | 1.145 | 1.166 | 1.188 | 1.210 |
3 | 1.030 | 1.061 | 1.093 | 1.125 | 1.158 | 1.191 | 1.225 | 1.260 | 1.295 | 1.331 |
4 | 1.041 | 1.082 | 1.126 | 1.170 | 1.216 | 1.262 | 1.311 | 1.360 | 1.412 | 1.464 |
5 | 1.051 | 1.104 | 1.159 | 1.217 | 1.276 | 1.338 | 1.403 | 1.469 | 1.539 | 1.611 |
6 | 1.062 | 1.126 | 1.194 | 1.265 | 1.340 | 1.419 | 1.501 | 1.587 | 1.677 | 1.772 |
7 | 1.072 | 1.149 | 1.230 | 1.316 | 1.407 | 1.504 | 1.606 | 1.714 | 1.828 | 1.949 |
8 | 1.083 | 1.172 | 1.267 | 1.369 | 1.477 | 1.594 | 1.718 | 1.851 | 1.993 | 2.144 |
9 | 1.094 | 1.195 | 1.305 | 1.423 | 1.551 | 1.689 | 1.838 | 1.999 | 2.172 | 2.358 |
10 | 1.105 | 1.219 | 1.344 | 1.480 | 1.629 | 1.791 | 1.967 | 2.159 | 2.367 | 2.594 |
11 | 1.116 | 1.243 | 1.384 | 1.539 | 1.710 | 1.898 | 2.105 | 2.332 | 2.580 | 2.853 |
12 | 1.127 | 1.268 | 1.426 | 1.601 | 1.796 | 2.012 | 2.252 | 2.518 | 2.813 | 3.138 |
13 | 1.138 | 1.294 | 1.469 | 1.665 | 1.886 | 2.133 | 2.410 | 2.720 | 3.066 | 3.452 |
14 | 1.149 | 1.319 | 1.513 | 1.732 | 1.980 | 2.261 | 2.579 | 2.937 | 3.342 | 3.797 |
15 | 1.161 | 1.346 | 1.558 | 1.801 | 2.079 | 2.397 | 2.759 | 3.172 | 3.642 | 4.177 |
16 | 1.173 | 1.373 | 1.605 | 1.873 | 2.183 | 2.540 | 2.952 | 3.426 | 3.970 | 4.595 |
17 | 1.184 | 1.400 | 1.653 | 1.948 | 2.292 | 2.693 | 3.159 | 3.700 | 4.328 | 5.054 |
18 | 1.196 | 1.428 | 1.702 | 2.026 | 2.407 | 2.854 | 3.380 | 3.996 | 4.717 | 5.560 |
19 | 1.208 | 1.457 | 1.754 | 2.107 | 2.527 | 3.026 | 3.617 | 4.316 | 5.142 | 6.116 |
20 | 1.220 | 1.486 | 1.806 | 2.191 | 2.653 | 3.207 | 3.870 | 4.661 | 5.604 | 6.727 |
21 | 1.232 | 1.516 | 1.860 | 2.279 | 2.786 | 3.400 | 4.141 | 5.034 | 6.109 | 7.400 |
22 | 1.245 | 1.546 | 1.916 | 2.370 | 2.925 | 3.604 | 4.430 | 5.437 | 6.659 | 8.140 |
23 | 1.257 | 1.577 | 1.974 | 2.465 | 3.072 | 3.820 | 4.741 | 5.871 | 7.258 | 8.954 |
24 | 1.270 | 1.608 | 2.033 | 2.563 | 3.225 | 4.049 | 5.072 | 6.341 | 7.911 | 9.850 |
25 | 1.282 | 1.641 | 2.094 | 2.666 | 3.386 | 4.292 | 5.427 | 6.848 | 8.623 | 10.835 |
26 | 1.295 | 1.673 | 2.157 | 2.772 | 3.556 | 4.549 | 5.807 | 7.396 | 9.399 | 11.918 |
27 | 1.308 | 1.707 | 2.221 | 2.883 | 3.733 | 4.822 | 6.214 | 7.988 | 10.245 | 13.110 |
28 | 1.321 | 1.741 | 2.288 | 2.999 | 3.920 | 5.112 | 6.649 | 8.627 | 11.167 | 14.421 |
29 | 1.335 | 1.776 | 2.357 | 3.119 | 4.116 | 5.418 | 7.114 | 9.317 | 12.172 | 15.863 |
30 | 1.348 | 1.811 | 2.427 | 3.243 | 4.322 | 5.743 | 7.612 | 10.063 | 13.268 | 17.449 |
31 | 1.361 | 1.848 | 2.500 | 3.373 | 4.538 | 6.088 | 8.145 | 10.868 | 14.462 | 19.194 |
32 | 1.375 | 1.885 | 2.575 | 3.508 | 4.765 | 6.453 | 8.715 | 11.737 | 15.763 | 21.114 |
33 | 1.389 | 1.922 | 2.652 | 3.648 | 5.003 | 6.841 | 9.325 | 12.676 | 17.182 | 23.225 |
34 | 1.403 | 1.961 | 2.732 | 3.794 | 5.253 | 7.251 | 9.978 | 13.690 | 18.728 | 25.548 |
35 | 1.417 | 2.000 | 2.814 | 3.946 | 5.516 | 7.686 | 10.677 | 14.785 | 20.414 | 28.102 |
36 | 1.431 | 2.040 | 2.898 | 4.104 | 5.792 | 8.147 | 11.424 | 15.968 | 22.251 | 30.913 |
37 | 1.445 | 2.081 | 2.985 | 4.268 | 6.081 | 8.636 | 12.224 | 17.246 | 24.254 | 34.004 |
38 | 1.460 | 2.122 | 3.075 | 4.439 | 6.385 | 9.154 | 13.079 | 18.625 | 26.437 | 37.404 |
39 | 1.474 | 2.165 | 3.167 | 4.616 | 6.705 | 9.704 | 13.995 | 20.115 | 28.816 | 41.145 |
40 | 1.489 | 2.208 | 3.262 | 4.801 | 7.040 | 10.286 | 14.974 | 21.725 | 31.409 | 45.259 |
41 | 1.504 | 2.252 | 3.360 | 4.993 | 7.392 | 10.903 | 16.023 | 23.462 | 34.236 | 49.785 |
42 | 1.519 | 2.297 | 3.461 | 5.193 | 7.762 | 11.557 | 17.144 | 25.339 | 37.318 | 54.764 |
43 | 1.534 | 2.343 | 3.565 | 5.400 | 8.150 | 12.250 | 18.344 | 27.367 | 40.676 | 60.240 |
44 | 1.549 | 2.390 | 3.671 | 5.617 | 8.557 | 12.985 | 19.628 | 29.556 | 44.337 | 66.264 |
45 | 1.565 | 2.438 | 3.782 | 5.841 | 8.985 | 13.765 | 21.002 | 31.920 | 48.327 | 72.890 |
46 | 1.580 | 2.487 | 3.895 | 6.075 | 9.434 | 14.590 | 22.473 | 34.474 | 52.677 | 80.180 |
47 | 1.596 | 2.536 | 4.012 | 6.318 | 9.906 | 15.466 | 24.046 | 37.232 | 57.418 | 88.197 |
48 | 1.612 | 2.587 | 4.132 | 6.571 | 10.401 | 16.394 | 25.729 | 40.211 | 62.585 | 97.017 |
49 | 1.628 | 2.639 | 4.256 | 6.833 | 10.921 | 17.378 | 27.530 | 43.427 | 68.218 | 106.719 |
50 | 1.645 | 2.692 | 4.384 | 7.107 | 11.467 | 18.420 | 29.457 | 46.902 | 74.358 | 117.391 |
51 | 1.661 | 2.745 | 4.515 | 7.391 | 12.041 | 19.525 | 31.519 | 50.654 | 81.050 | 129.130 |
52 | 1.678 | 2.800 | 4.651 | 7.687 | 12.643 | 20.697 | 33.725 | 54.706 | 88.344 | 142.043 |
53 | 1.694 | 2.856 | 4.790 | 7.994 | 13.275 | 21.939 | 36.086 | 59.083 | 96.295 | 156.247 |
54 | 1.711 | 2.913 | 4.934 | 8.314 | 13.939 | 23.255 | 38.612 | 63.809 | 104.962 | 171.872 |
55 | 1.729 | 2.972 | 5.082 | 8.646 | 14.636 | 24.650 | 41.315 | 68.914 | 114.408 | 189.059 |
56 | 1.746 | 3.031 | 5.235 | 8.992 | 15.367 | 26.129 | 44.207 | 74.427 | 124.705 | 207.965 |
57 | 1.763 | 3.092 | 5.392 | 9.352 | 16.136 | 27.697 | 47.302 | 80.381 | 135.928 | 228.762 |
58 | 1.781 | 3.154 | 5.553 | 9.726 | 16.943 | 29.359 | 50.613 | 86.812 | 148.162 | 251.638 |
59 | 1.799 | 3.217 | 5.720 | 10.115 | 17.790 | 31.120 | 54.156 | 93.757 | 161.497 | 276.801 |
60 | 1.817 | 3.281 | 5.892 | 10.520 | 18.679 | 32.988 | 57.946 | 101.257 | 176.031 | 304.482 |
61 | 1.835 | 3.347 | 6.068 | 10.940 | 19.613 | 34.967 | 62.003 | 109.358 | 191.874 | 334.930 |
62 | 1.853 | 3.414 | 6.250 | 11.378 | 20.594 | 37.065 | 66.343 | 118.106 | 209.143 | 368.423 |
63 | 1.872 | 3.482 | 6.438 | 11.833 | 21.623 | 39.289 | 70.987 | 127.555 | 227.966 | 405.265 |
64 | 1.890 | 3.551 | 6.631 | 12.306 | 22.705 | 41.646 | 75.956 | 137.759 | 248.483 | 445.792 |
65 | 1.909 | 3.623 | 6.830 | 12.799 | 23.840 | 44.145 | 81.273 | 148.780 | 270.846 | 490.371 |
66 | 1.928 | 3.695 | 7.035 | 13.311 | 25.032 | 46.794 | 86.962 | 160.682 | 295.222 | 539.408 |
67 | 1.948 | 3.769 | 7.246 | 13.843 | 26.283 | 49.601 | 93.049 | 173.537 | 321.792 | 593.349 |
68 | 1.967 | 3.844 | 7.463 | 14.397 | 27.598 | 52.577 | 99.563 | 187.420 | 350.753 | 652.683 |
69 | 1.987 | 3.921 | 7.687 | 14.973 | 28.978 | 55.732 | 106.532 | 202.413 | 382.321 | 717.952 |
70 | 2.007 | 4.000 | 7.918 | 15.572 | 30.426 | 59.076 | 113.989 | 218.606 | 416.730 | 789.747 |
71 | 2.027 | 4.080 | 8.155 | 16.194 | 31.948 | 62.620 | 121.969 | 236.095 | 454.236 | 868.722 |
72 | 2.047 | 4.161 | 8.400 | 16.842 | 33.545 | 66.378 | 130.506 | 254.983 | 495.117 | 955.594 |
我們把這個6%的例子畫出來,我們可以得到曲線不是直線,而是曲線,所以可以看到每12年會翻倍,
所以我們粗略可以知道,小孩在12歲、24歲、36歲、48歲、60歲、72歲會一直翻倍。
也對應 2元、4元、8元、16元、32元、64元。
但其實可以發現真正的數字是2.012、4.049、8.147、16.394、32.988、66.378
也就是複利越久,其實翻倍的時間是會縮短的。
大家是不是趕快幫小孩存一筆成長基金呢。
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