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贾的菜 · 2022年04月09日

有点糊涂了

  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

请问Account1的计算为什么不能按照每年末存入750、存3年来理解，即PMT=750，N=12，I/Y=3/4。是否因为Account1有资金存入的时间点为下一年的年初？若是这样，Account1能否按先付年金存2年来理解？

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星星_品职助教 · 2022年04月09日

同学你好，

1）根据题干，Account 1的计算是“每年末存入750、存3年”，不能理解为先付年金。

2）“PMT=750，N=12，I/Y=3/4” 这个列式代表的是每个季度都存入750，对应12个季度和季度利率3/4。如果是每年的情况，列式应为PMT=750，N=3，I/Y=3.03（EAR转化后的年利率）

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