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imxhan · 2020年06月01日

问一道题：NO.PZ2018062016000012

  1. CFA I
  2. Quantitative

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.

请问为什么答案中the present value of Plan B is $900/(5%/4)=$72,000？是用的哪一个公式？

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2 个答案

星星_品职助教 · 2022年05月31日

@18816562889

同学你好，已在独立的问题里回复。没有名义季度利率这个东西，名义年利率 / 期数=实际期间利率。

问题只提一次就可以了。

星星_品职助教 · 2020年06月01日

同学你好，

这道题要求的是“perpetuity ”即永续年金的现值，所以公式需要用到永续年金公式PV=C/r，其中C是期间现金流即本题中的每季度支付900，而r是相对应的期间利率，在本题中即是季度利率。

答案中公式分母的5%/4对应的就是将“ stated annual rate is 5% and compounded quarterly”转化为期间利率即季度利率。

 

18816562889 · 2022年05月31日

老师，请问题目给出的是名利年利率，那么除以4，得出的也是名义季度利率。但是我们计算不都用实际利率而不是名义吗？所以应该把名义季度利率再转化成实际季度利率再进行计算？

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