CFA复利奥秘之72法则
2016-01-13
摘要金融学上有所谓72法则,用来速算投资倍增所需的时间,反映出的是复利的结果。 当我们在做财务规划时,了解复利的运作和计算是相当重要的。我们常喜欢用利滚利来形容某项投资获利快速、报酬惊人,比方说拿1万元去买年报酬率20%的股票,若一切顺利,约莫3年半
金融学上有所谓72法则,用来速算投资倍增所需的时间,反映出的是复利的结果。
当我们在做财务规划时,了解复利的运作和计算是相当重要的。我们常喜欢用“利滚利”来形容某项投资获利快速、报酬惊人,比方说拿1万元去买年报酬率20%的股票,若一切顺利,约莫3年半的时间,1万元就变成2万元。复利的时间乘数效果,更是这其中的奥妙所在。
把复利公式摊开来看,“本利和=本金×(1+利率)^期数”这个“期数”时间因子是整个公式的关键因素,一年又一年(或一月一月)地相乘下来,数值当然会愈来愈大。虽然复利公式并不难理解,但若是期数很多,算起来还是相当麻烦,于是市面上有许多理财书籍,都列有复利表,投资人只要按表索骥,很容易便可计算出来。不过复利表虽然好用,但也不可能始终都带在身边,若是遇到需要计算复利报酬时,倒是有一个简单的“72法则”可以取巧。
所谓的“72法则”就是以1%的复利来计息,经过72年以后,你的本金就会变成原来的一倍。例如:利用5%年报酬率的投资工具,经过14.4年(72/5)本金就变成一倍;利用12%的投资工具,则要6年左右(72/12),才能让1块钱变成2块钱。因此,今天如果你手中有100万元,运用了报酬率15%的投资工具,你可以很快便知道,经过约4.8年,你的100万元就会变成200万元。
假设较初投资金额为100元,复息年利率9%,利用“72法则”,将72除以9(增长率),得8,即需约8年时间,投资金额滚存至200元(两倍于100元),而准确需时为8.0432年。
虽然利用72法则不像查表计算那么精确,但也已经十分接近了,因此当你手中少了一份复利表时,记住简单的72法则,或许能够帮你不少的忙。
那为什么是72呢?我们知道复利增长的极限是e。如果本金是100,复利是x,时间是t。可以得到公式:
![](data:image/jpeg;base64,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)
当我们在做财务规划时,了解复利的运作和计算是相当重要的。我们常喜欢用“利滚利”来形容某项投资获利快速、报酬惊人,比方说拿1万元去买年报酬率20%的股票,若一切顺利,约莫3年半的时间,1万元就变成2万元。复利的时间乘数效果,更是这其中的奥妙所在。
把复利公式摊开来看,“本利和=本金×(1+利率)^期数”这个“期数”时间因子是整个公式的关键因素,一年又一年(或一月一月)地相乘下来,数值当然会愈来愈大。虽然复利公式并不难理解,但若是期数很多,算起来还是相当麻烦,于是市面上有许多理财书籍,都列有复利表,投资人只要按表索骥,很容易便可计算出来。不过复利表虽然好用,但也不可能始终都带在身边,若是遇到需要计算复利报酬时,倒是有一个简单的“72法则”可以取巧。
所谓的“72法则”就是以1%的复利来计息,经过72年以后,你的本金就会变成原来的一倍。例如:利用5%年报酬率的投资工具,经过14.4年(72/5)本金就变成一倍;利用12%的投资工具,则要6年左右(72/12),才能让1块钱变成2块钱。因此,今天如果你手中有100万元,运用了报酬率15%的投资工具,你可以很快便知道,经过约4.8年,你的100万元就会变成200万元。
假设较初投资金额为100元,复息年利率9%,利用“72法则”,将72除以9(增长率),得8,即需约8年时间,投资金额滚存至200元(两倍于100元),而准确需时为8.0432年。
虽然利用72法则不像查表计算那么精确,但也已经十分接近了,因此当你手中少了一份复利表时,记住简单的72法则,或许能够帮你不少的忙。
那为什么是72呢?我们知道复利增长的极限是e。如果本金是100,复利是x,时间是t。可以得到公式:
来自:金程CFA