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叶赫那拉坤坤 · 2020年02月10日

问一道题：NO.PZ2015120604000170

  1. CFA I
  2. Quantitative

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 interestt rate is 5.5% annually, and A.J. will make payments at the end of each year, how much would A.J. put aside?

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

第一步能用先付年金计算吗？


学费不是期初缴纳吗？ n=4 i=5.5 pmt=-22000 fv=0 bng cpt pv=81354.53


然后第二步用后付年金计算

n=15 i=5.5 pv=0 fv=81354.53 cpt pmt= 3630.49

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Crystalsuiwei · 2020年02月16日

我知道答案的算法，但是我也跟这个同学一样考虑他那种算法，但是为什么答案就不同了呢？从道理上说，两种算法应该一样的结果。请进一步解释。

星星_品职助教 · 2020年02月16日

重述一遍，这种题目有固定的的解题思路，按照考试思路即可。以下了解就行：1. 这道题的核心是15-18有四笔现金流要求PV，并不涉及到学费是先付还是后付的问题 2. 即使先付年金算到15时间点，答案也不会有不同，因为无论怎么算，PMT都只能有14笔，否则在15时间点就会出现又付钱又存钱的情况。所以如果用先付年金算到N=15，还得在再除以1+r折到14时间点，然后再按照同样的step 2来计算PMT 3. 按照你的算法的话，是有15笔PMT，所以和14笔PMT的金额肯定是不一样的，这是对不上的原因。4. 这是固定的考法，不用纠结

1 个答案

星星_品职助教 · 2020年02月11日

同学你好，

这道题告诉了 starting 15 years from now，就不用考虑学费是什么年金的问题了，四笔学费的现金流发生时间就是15,16,17,18.

然后再根据这四笔现金流算PV，从这个角度来讲，用后付年金可以使现金流连贯，正好接上。

这种题型是有固定的考法和对应做法的，可以参照答案解析。课上也讲了一道几乎一样的例题。

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