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Yuki119808 · 2023年03月06日

为什么不能用，pmt=-750,pv=0,n=12,I/Y=0.75 算 account 1 的FV

  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

为什么不能用，pmt=-750,pv=0,n=12,I/Y=0.75 算 account 1 的FV

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3 个答案

星星_品职助教 · 2023年06月28日

@sonyasoong

题干中标出3%为“stated”的利率，即该利率只是一个名义上的利率，仅用于报价和对比。换而言之，这个名义上的3%是由实际的季度利率*4得到的。

所以需要将3%转化为实际利率后才能计算。EAR即为实际的年度利率。

星星_品职助教 · 2023年03月07日

@Yuki119808

可以将这三者统一为以年为单位，然后计算器直接按出来。

PMT=750不变，N此时不再是12个季度，而是3年。利率也转化为年度利率（即EAR）。（1+3%/4）4-1=3.034%，则I/Y=3.034.

这个背景下的计算器按键为：

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

sonyasoong · 2023年06月28日

为什么要转化为EAR？而不直接用3%

星星_品职助教 · 2023年03月07日

同学你好，

PMT、N、I/Y这三个要素是一致的。如果如提问中的列式（N=12个月，I/Y为月利率），就相当于每个月都付750，而不是每年付750.

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