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Sissiwonglx · 2022年08月18日

FV PV的理解

  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.

老师，我在这里的理解是PV=0 求future value

求老师纠正

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1 个答案

星星_品职助教 · 2022年08月18日

同学你好，

这道题本身只有7笔中间现金流（PMT），起点和终点都没有独立的现金流。

类似这类题目，如果题目求的是PV，则就是将所有PMT的现金流折现到0时点。此时FV为0，PV是算出来的值。

如果求FV，则此时FV是所有PMT现金流复利出来算出的值，此时按计算器的PV才为0.

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观察本题的问法：“What is the difference of account present value.....”，发现是要计算PV，所以此时PV一定是算出来的值，不会为0.

在这个问法的背景下，按计算器时，FV就是0了。

END模式下，计算器按键为：N=7, I/Y=4, PMT=500, FV=0, then PV=-3001.03。

如果求先付年金的PV则只需要将模式调为BGN即可。

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