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当如匠人 · 2020年06月05日

问一道题：NO.PZ2018062016000010

  1. CFA I
  2. Quantitative

问题如下：

Mary has a separate account for her annual savings which has a stated annual rate of 3% and compounding quarterly. At the end of each year, she transfers unequal cash flows into this account. Year 1: $500, Year 2: $800, Year 4: $300, Year 5: $500. How much will Mary save for her account at the end of year 5?

选项：

A.

$2246.81

B.

$2247.65

C.

$2281.00

解释：

B is correct.

No.PZ2018062016000010 (选择题)

Mary has a separate account for her annual savings which has a stated annual rate of 3% and compounding quarterly. At the end of each year, she transfers unequal cash flows into this account. Year 1: $500, Year 2: $800, Year 4: $300, Year 5: $500. How much will Mary save for her account at the end of year 5?

正确答案是: B

A

$2246.81

B

$2247.65

C

$2281.00

老师，请问这道题中为何不需要先把 stated annual rate of 3%通过公式EAR=(1+3%/4)^4*5-1=0.161184,把EAR计算出来后再按答案的列表一一计算呢？如第一个的FV=500（1+EAR）^4=909.02。

谢谢，不知这是在讲义上哪里有提到过，这个知识点学得很迷茫

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1 个答案

星星_品职助教 · 2020年06月05日

同学你好，

你计算的EAR并不是一个一年的利率，而是一个5年的值。但后续列举的FV=500（1+EAR）^4这里面用的EAR，是一个一年的EAR，用来复利4年。

所以可以在你的计算基础上做个小幅修正，EAR=(1+3%/4)^4-1=0.0303，第一个FV=500（1+EAR）^4=563.5，其余的以此类推即可。

这个知识点就是EAR+已知PV求FV的应用，算熟练了就好了

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