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西红柿面 · 2023年04月24日

为什么不需要计算EAR？

  1. CFA I
  2. Quantitative

NO.PZ2018062016000012

问题如下：

David is going to retire in ABC company. The company has two retirement plans: Plan A is a one-time total retirement fund of $70,000, Plan B is a perpetuity of $900 at the end of each quarter that stated annual rate is 5% and compounded quarterly. Which plan should David choose?

选项：

A.

There is no difference

B.

Plan A

C.

Plan B

解释：

C is correct. The present value of Plan B is $900/(5%/4)=$72,000, which is larger than $70,000, the present value of Plan A. Therefore, David should choose Plan B.

既然是按季度计息的，为什么不应该是先把1+EAR=(1+5%/4)的四次方， 算出来EAR=5.0945%然后再除以4是每期利率，再用900除以这个每期利率吗？


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星星_品职助教 · 2023年04月24日

同学你好，

1）期间利率=名义利率(stated annual interest rate) / 计息频率。即本题季度利率就是5%/4；

2）EAR是根据复利计息所计算得出的实际利率，并不能再（以单利的形式）去除以计息频率。能除以计息频率的只有stated annual interest rate。

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