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Ash · 2022年07月18日

PV&FV

  1. CFA I
  2. Quantitative

NO.PZ2018062016000013

问题如下：

You plan to set a saving account for 7 years which annual discount rate is 4% and compounded annually. Each year $500 cash is transferred into this account. What is the difference of account present value between transferring the cash at the beginning and at the end of each year?

选项：

A.

$500.00

B.

$120.04

C.

$115.42

解释：

B is correct. If the cash is transferred at the beginning, set the calculator in the BGN mode and input data: N=7, I/Y=4, PMT=500, FV=0, then PV=-3121.07. If the cash is transferred at the end, set the calculator in the END mode and input data: N=7, I/Y=4, PMT=500, FV=0, then PV=-3001.03. Therefore, the difference between the two methods is 3121.07-3001.03=$120.04.

做一个a aving acc, 不是应该PV为0吗，为什么设FV为0？

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2 个答案

星星_品职助教 · 2022年07月19日

@Ash

1）要看题目要求的是什么。如果求的是PV，那么无论题干如何描述，无论是什么account，PV都不可能是0，而是需要去计算的。

这个方式可以用来简单粗暴的判断，不至于做错题目。

2）这里的PV不能理解为期初有没有独立的现金流。否则因为没有期初独立现金流，就会得出PV=0的错误结论。上述思路是求FV时的思路，不能用于计算PV的题目。

3）本题的PV应理解为：一个账户每年往里面存500，连续存7年，那么这些钱换算到今天，相当于是值多少钱。

从这个角度出发去理解，就不会认为PV=0了。

星星_品职助教 · 2022年07月18日

同学你好，

这道题要计算就是年金的现值，所以PV不可能设为0，否则就没法算了。

FV指的是在年金的末期是否有独立的一笔现金流存在，本题没有，所以FV=0。

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补充1：如果是要计算债券的PV，债券在到期日往往会有一笔单独的本金的流入，此时FV就不是0了，而是需要输入本金的值。类似的题目可以在固收科目中见到；

补充2：如果本题要计算的不是PV而是FV，那么此时按计算器时，由于期初没有独立的一笔现金流流入，所以此时PV才能设置为0.

Ash · 2022年07月19日

感觉题目出的不是太好，问题中要解决的是PV比较，但题干中提到的是初始设一个saving acc, 然后每年往里打钱，从逻辑上来说PV是0才合适，有点confusing

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