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Seabiscuit · 2020年08月16日

问一道题：NO.PZ2018062016000019 [ CFA I ]

  1. CFA I
  2. Quantitative

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

leave all money in account 2的意思不是说把每年的pmt=750也放在account 2里吗？那是不是应该pv=-30000，pmt=750，n=3，i/y=2.5，然后求fv

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1 个答案

星星_品职助教 · 2020年08月16日

同学你好，

leave all money in account 2的意思如果不把利息拿走，只是正常按照compounded annually with annual interest rate of 2.5%的方式投资的话，3年后account 2里会有多少钱。

这个时候不存在PMT的概念，因为750这个时候直接利滚利的在account 2里投资了，不存在往外拿走利息这个步骤了。也就是PMT=0。但如果按照你那个按键方式，实质还是每年把利息750拿出account 2，这就不是“Leave all the money in Account 2”的含义了。

正确按键应为： PV=-30,000，PMT=0，N=3，I/Y=2.5，CPT FV=32,306.72。这个的含义就是一开始有30,000，按照2.5%的利率复利投资利滚利的滚三年，能拿到多少钱。是一个简单直白的已知PV求FV的single cash flow 问题。

所以如果leave all money in account 2就可以得到32,306.72这么多钱，然后再和原始的那种方案比较，算出一个差值即可。

 

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