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lalalala · 2023年02月25日

题目中的2.5%为什么要÷365之后才能作为I/Y

  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.

理解先求EAR再计算器的做法，但是第二种解法（直接使用计算器的方法）中，I/Y=2.5/365，这里不明白，2.5%为什么要÷365之后才能作为I/Y？题目中“stated annual interest rate of 2.5%.”不也是年为单位吗。

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1 个答案

星星_品职助教 · 2023年02月25日

同学你好，

stated annual interest rate只是用来报价的名义利率，不能直接使用。计算时需要转化为真实的期间利率，即本题中的日利率I/Y=2.5/365。

这才是需要计算EAR的原因，否则直接用stated annual interest rate当做年利率就可以了。

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