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jvniki · 2022年12月15日

这道题的思路终于有了一点

  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

我想到了，应该保持期数和利率的一致性，但我是按照每个季度的利率，把PMT 、N、I/Y 都转化成了季度

PMT = 750/4 = 187.5

N = 3*4 = 12

I/Y = 3%/4

PV = 0

求FV


我不太理解 什么时候应该转换成年，什么时候又是季度展示

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已采纳答案

星星_品职助教 · 2022年12月17日

同学你好，

每年750的PMT是每年年末时点产生的一整笔金额，并不是年中不同时点里产生的四笔金额。所以不能简单的除以4，会涉及到货币时间价值上的问题。

由于PMT、I/Y、N这三者必须一致，而年度的PMT又无法简单转化，所以思路转为保持年度的PMT 750不变，将I/Y转化为EAR，同时保持N为3年不变

这种处理方式同样达到了三者一致（都是年度的概念），就可以计算了。

最终解题步骤为：

①（1+3%/4）4-1=3.034%，则I/Y=3.034.

②计算器按键为：

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

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