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LilyRosemary · 2022年03月15日

为什么I/Y不能直接用给出来的stated annul interst rate2.5%，而是等于EAR？

  1. CFA I
  2. Quantitative

NO.PZ2018062016000006

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.

为什么I/Y不能直接用给出来的stated annul interst rate2.5%，而是等于EAR？

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1 个答案

星星_品职助教 · 2022年03月15日

同学你好，

stated annual interest rate的意思就是名义上的报价利率。从名字上就可以看出它只是一个名义上的报价，并不是实际的利率，所以只有转化后才能使用。

转化的方法是先将其转化为期间利率，例如本题就应转化为（实际）日利率 2.5%/365。

此后是否转化为EAR要看题目的要求，本题由于要求的是有多少“年”，所以转为EAR可以直接得出N，

PV=-1，PMT=0，FV=2，I/Y=2.531（EAR转化后的结果），CPT N=27.73直接得到答案A。

也可以直接使用日利率，计算器按法为：

PV=-1，FV=2，PMT=0，I/Y=2.5/365=0.0068，CPT N=10,120.295

（天）

转化成年就是/365=27.7268。

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