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Nimo. · 2023年05月24日

有点读不懂题，她到底对1和2干了啥呀？

  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

有点读不懂题，她到底对1和2干了啥呀？Clark put the principal of $30,000 to Account 2 and annual interest to Account 1 as long as he received. 这句话怎么理解呢？谢谢老师！

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星星_品职助教 · 2023年05月24日

同学你好，

这句话的意思是当Account 2中产生利息后，立刻就把利息部分转到Account 1中去。

所以，Account 2中每年产生的750利息（30,000×2.5%=750）就不参与Account 2中的复利，而是直接被转到Account 1中参与复利。3年中，Account 2一共会产生3笔750的利息。从Account 1的角度来看，这就相当于从第一年末开始，每年固定流入750，即一个PMT=750的3年期年金。

所以，Account 1的终值为：PV=0；I/Y=3.034；N=3；PMT=750；CPT FV=-2,318.95，其中I/Y对应EAR，EAR=（1+3%/4）4-1=3.034%。

对于Account 2来说，30,000的本金是一直不动的，利息产生后就立刻被转走，也不参与利滚利。即3年后，Account 2中还是只有最初的30,000.

所以两个账户最终的FV为：Account 1（2,318.95）+Account 2（30,000）=32,318.95

Nimo. · 2023年05月28日

谢谢老师，我读懂了这个意思了。还有一个小问题，I/Y=3.034是怎么算出来的呀？麻烦老师了！

星星_品职助教 · 2023年05月28日

@Nimo.

本题的PMT 750是一年一付，所以对应的I/Y同样也需要是年度的值。

故转化为EAR。根据Account 1中的“ stated annual rate of 3%,”可得r=3%，根据“compounded quarterly”，取m=4。代入EAR的公式即可得到结果。

上述计算即回复中的如下部分：

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