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Swan陈师雯 · 2021年03月30日

这道题可以理解为：后付年金的形式 连续三年每年固定PMT为750，1/y=0.75 PV=0 求FV吗？计算出来结果是错的

  1. CFA I
  2. Quantitative

NO.PZ2018062016000019

问题如下：

Clark opens two bank accounts. Account 1 is compounded quarterly with stated annual rate of 3%, while Account 2 is compounded annually with annual interest rate of 2.5%. Clark put the principal of $30,000 to Account 2 and annual interest to Account 1 as long as he received. After three years, what is the difference between Clark’s current wealth planning and leaving all the money in Account 2?

选项：

A.

$13.50

B.

$12.24

C.

$16.12

解释：

B is correct.

Annual interest received from Account 2 is $30,000*2.5%=$750.

After three years, Clark’s current wealth planning:

Leave all the money in Account 2: $30,000*(1+2.5%)3=$32306.71

The difference is $32318.95-$32306.71=12.24

这道题可以理解为：后付年金的形式

连续三年每年固定PMT为750，1/y=0.75 PV=0 求FV吗？计算出来结果是错的

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已采纳答案

星星_品职助教 · 2021年03月30日

同学你好，

如果题干中没有明确的说明PMT支付的时间是today/now/at the beginning of the year等，都按照后付计算，例如本题。后付年金的计算占了绝大多数。

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“连续三年每年固定PMT为750，1/y=0.75 PV=0 求FV”的这个计算里没有写出N的取值。

①如果是按照N为连续3年即N=3计算。问题在于I/Y的期限和N不匹配。

根据题干对于利率的描述：“….compounded quarterly with stated annual rate of 3%”。如果I/Y=0.75，则对应利率的计算为3%/4=0.75%，这是一个“季度”利率；

但根据题干对于N的描述：“After three years….”。N对应的是3“年”

所以这样计算是错误的。使用计算器的前提是I/Y & N & PMT三者的期限必须统一。


②如果按照N=3×4=12计算，也是错的。因为此时N和I/Y都是季度的概念了，但是PMT=750是年度概念。

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本题最方便的方式是将三者都转化为“年度”的概念。PMT=750不变，N是3年。利率也转化为年度利率（即EAR）。（1+3%/4）4-1=3.034%，则I/Y=3.034.

所以正确的计算器按键为：

PV=0；I/Y=3.034；N=3；PMT=750；CPT FV=-2,318.95

然后加上account中原有不变的30,000即可得到表格中的32,318.95.

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