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菡萏琼琚 · 2022年05月03日

老师后付年金的PV为什么不是零呢

  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.

题干当中说存7年钱，算先付和后付的PV的差值，那后付就是第一年年初PV没钱呀，那PV应该是0吧，先付的时候就是在第一年年初付，那PV就是500呀，那差值应该是500呀。

老师我这么想的话是哪里不对吗，为什么不能这么算呢？

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已采纳答案

星星_品职助教 · 2022年05月03日

同学你好，

先付和后付的区别在于PMT的时间点。本题的500是PMT的概念，并不是PV。

PV是所有PMT现金流的折现值，即本题要考虑所有的7笔PMT，不能只考虑第一笔。

所以需要在先付和后付模式下各自算出一个PV，然后做减法。

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