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Quadradinho · 2019年11月18日

问一道题：NO.PZ2018062016000013

  1. CFA I
  2. Quantitative

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.

可以直接算差额吗？相当于少了一个1+4%。500*（1+4%）的结果。

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1 个答案

星星_品职助教 · 2019年11月18日

同学你好，

直接算差额是个非常好的思路。但差额不是500*(1+4%)。先付年金的现值PV BGN=PV END*（1+4%）,（这也是上课时老师讲的计算器不用调到BGN模式的另一种先付年金现值的算法）。所以差额为PV BGN-PV END=PV END*4%。计算器算出PV END=3001.03，然后即可得出差额为120.04即B选项。

算差额的想法非常好。如果已经对于先付年金和后付年金很熟悉了，考试的时候可以直接算差额省时间。如果对于两种模式不熟，可以像答案解析那样先算一个先付，再算一个后付，直接做差，也能确保答案正确，加油~

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