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AgnesWu · 2023年05月29日

请问

  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

我想得比较复杂，本金在账户2里面不需要按照2.5%复利吗

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已采纳答案

星星_品职助教 · 2023年05月29日

同学你好，

1）本金30,000会在Account 2里每年产生30,000×2.5%=750的利息；

2）这750的利息不在Account 2中参与复利。按照题干描述，在每笔利息产生的同时，这个750就会被转移到Account 1中（...annual interest to Account 1 as long as he received）。从此就按照Account 1的利率参与复利，和Account 2再无关系。

所以，Account 2中一直只有原本金30,000，利息一产生就被划走，到最后依然是30,000不变。

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