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wishwind · 2020年11月07日

问一道题：NO.PZ2018062016000010 [ CFA I ]

  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.

这道题一定要列表一年年算出来再加总吗？还是先算NPV，再复利五年更简便易行？考试建议哪个方案又快又不容易出错？
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2 个答案

星星_品职助教 · 2021年01月14日

同学你好，

NPV并不是常规的解题思路。不建议这么算。

如果NPV算出来是2057.24，说明你用的利率是3%/4=0.75%。这是一个季度利率。但同时输入的现金流都是年度现金流。

所以需要首先转化为年度利率(1+3%/4)^4-1=3.03%。这时候计算出来的NPV=1935.845

此外由于这么算出来的是NPV，题目要求计算的是第五年后的FV（ at the end of year 5），所以NPV还需要复利到5年后。

1935.845×(1+3.03%）^5=2247.45。选择B选项。细微的差异源自四舍五入。

 

星星_品职助教 · 2020年11月07日

同学你好，

考试的时候让算5年的可能不大，一般是3年居多。

NPV不是这种类型的题目的典型的算法，但也不用画表格。考试的时候简单画个数轴，标出来时间点，然后逐笔算出来加总这种方法比较常用。

· 2021年01月14日

这个可以使用计算器CF来完成的吗？但是我直接cf0=0，cf1=500，cf2=800，cf3=0，cf4=300，cf5=500，npv算出来是2057.242431？这是为啥？

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