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朱明远 · 2020年07月23日

问一道题：NO.PZ2018062016000006

  1. CFA I
  2. Quantitative

问题如下：

Lucy believes that after retirement she will need about $2 million totally for her daily expenses. At present, she has $1million investment at a stated annual interest rate of 2.5%. Assuming compounded daily, how long does it take for Lucy to have enough money for retirement life?

选项：

A.

27.73 years

B.

28.07 years

C.

26.48 years

解释：

A is correct.

EAR=(1+0.025/365)365-1=0.02531

$1million*(1+0.02531)N =$2million, N=27.73 years.


用计算器算的时候，I/Y=2.5/365


而从state rate 转换成EAR的时候，公式是（1+2.5%/365）^365-1


这两个都是算EAR吗？

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3 个答案

星星_品职助教 · 2020年08月01日

@ zzm

可以用这两种方法来算，这两种方法实质是一样的，只是你列的第一种方法多了一步由日利率转化EAR。形式上的差别在于如果用EAR，对应的N就要是多少年。如果用日利率，对应的N就是多少天，

这道题转化成EA计算R比较麻烦，直接用第二种方法的日利率按计算器算N，然后除以365就可以。

星星_品职助教 · 2020年07月31日

@ zzm

题干明确说明“ stated annual interest rate of 2.5%”，即2.5%只是一个名义上的利率，无法直接用这个利率来计算，所以需要将其转化为日利率，或有效年利率来进行下一步计算。

星星_品职助教 · 2020年07月24日

同学你好，

用计算器的那种方法转化的利率是期间利率，以本题为例，I/Y=2.5/365代表的是日利率。

而EAR是有效“年”利率的概念，对应期间是一年。第二种用公式转化的方式才是EAR。

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