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沐沐的方盒 · 2022年02月08日

这题我直接用计算器按年金方法按的，算出来是28.07，我想问问什么时候要算EAR，什么时候直接代入r就行？有点分不清

  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.

如题

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2 个答案

星星_品职助教 · 2022年02月09日

同学你好，

1）当题干中出现“ a stated annual interest rate of ..... assuming compounded ....”的描述，即为明显的要求去做转化的提示。

2）转化要优先转为期间利率，例如本题优先转化为2.5% / 365；然后根据题目决定是否要进一步转化为EAR；

3）本题转化为EAR的原因为三个选项都是以年为单位，所以选择EAR可以直接出答案；也可以直接算出有多少天，再除以365天得到年数

4）这种题目统一用计算器直接CPT N，不需要用Ln去解。

海胆君 · 2022年02月08日

compond daily，所以用每年复利一次的2.5%年化利率不合适了，你需要计算一个更精确的每日复利一次的利率，所以要先算EAR，从结果来看，EAR因为复利次数更多所以rate更大，这也是为什么2.5%算完的N比EAR的N大的原因。

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