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zhouanne · 2022年11月30日

先付后付

  1. CFA I
  2. Quantitative

NO.PZ2015120604000170

问题如下：

A.J. plans to pay his child's tuition fee for four years starting 15 years from now. He estimates the fees is $22,000 per year. If the saving account interest rate is 5.5% annually, and how much payment A.J. should make at the end of each year from now?

选项：

A.

$3,441.23

B.

$3,800.07

C.

$4,009.08

解释：

B is correct.

Step 1: N = 4, FV = 0, I/Y = 5.5, PMT = 22,000, CPT PV = -77,113.30

Step 2: PV =0, N = 14, I/Y = 5.5, FV = 77,113.30, CPT PMT =-$3,800.07

老师 这道题我如果先用先付年金计算在用后付年金计算可以吗

但是我算出来的不对啊



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1 个答案

星星_品职助教 · 2022年12月01日

同学你好，

第二步列式中，N=14，即一共有14期。但FV是15时点的值，这样计算相当于把发生在15时点的值人为放在了14时点，所以答案对不上。

如果要这样做，需要在第二步将FV15再折现一期到14时点，即81,354.53/1.055=77,113.30。此后N=14，I/Y=5.5，PV=0，计算出PMT。

可以看出上述方法是没有必要的，所以直接使用后付年金计算就可以。这类题目的常规解法都是后付。

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NO.PZ2015120604000170问题如下 A.J. plans to phis chils tuition fee for four years starting 15 years from now. He estimates the fees is $22,000 per year. If the saving account interest rate is 5.5% annually, anhow mupayment A.J. shoulmake the enof eayefrom now? A.$3,441.23B.$3,800.07C.$4,009.08B is correct.Step 1: N = 4, FV = 0, I/Y = 5.5, PMT = 22,000, CPT PV = -77,113.30Step 2: PV =0, N = 14, I/Y = 5.5, FV = 77,113.30, CPT PMT =-$3,800.07老师，我发现我做类似的题最容易做错的部分就是前面一个时间段短年份数，就像这道题，我就会按照15年来计算。

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