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iamjj · 2022年11月25日

不需要先算EAR吗

  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.

虽然答案相似，但是不是应该先把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？

还说这种题就近似用5%/4 当做每期利率就可以了？

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1 个答案

星星_品职助教 · 2022年11月25日

同学你好，

1）EAR已经是实际的利率，不能再除以4。只有名义上的报价利率（stated annual interest rate，如本题的“ stated annual rate is 5%”）才需要除以对应的计息频率，转化为实际的期间利率；

2）5%/4计算出来的是实际的季度利率，不是近似的利率；

综上，直接用季度PMT900，除以对应的实际季度利率5%/4，就可以计算出永续年金的现值。

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