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Tse0507 · 2023年01月15日

没看懂解析

  1. CFA I
  2. Quantitative

NO.PZ2018062016000014

问题如下：

Tom has twin daughters Lucy and Lily at 12 years old. Six years later, both will study in a famous university in California for four years with a tuition fee of $6,000 paid at the beginning of each year per person. Assume the annual discount rate is 5%, today Tom should prepare:

选项：

A.

$16,670

B.

$33,340

C.

$31,753

解释：

B is correct. Six years later, Tom will pay tuition fee of $12,000 each year and last for 4 years, as he has two daughters. The payment is paid in the front, therefore set the calculator at BGN mode and input: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition fund at year 6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.

按照答案写的计算顺序，第一步计算N=4, I/Y=5%, PMT=12,000, FV=0, then PV是44678.98，这里为什么用先付年金的公式呢，交学费的类似题目，比如讲义P17页的例题中第一步计算器也是用后付年金的公式，按照例题思路第二步用计算器n应该是5啊，为啥是6

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1 个答案

星星_品职助教 · 2023年01月15日

同学你好，

根据题干，可知首笔学费的现金流会在6时间点支付。如果用先付年金求现值，则现值也是求到首笔现金流的支付时刻，也就仍是6时间点。这样做下一步折现的N就是6。

上述做法不推荐，建议用后付年金的方式来解题：

END mode：

Step 1：PMT=12,000，N=4，FV=0，I/Y=5，CPT PV=-42,551.41。后付年金的折现是折到首笔现金流的前一期，也就是5时间点。所以下一步折现的N就是5.

Step 2：N=5，FV=42,551.41，I/Y=5，PMT=0，CPT PV=-33,340.14

常规的解题思路都是用后付年金。答案解析中的先付年金不是常规做法，在一些题型中会导致不必要的麻烦，仅做简单了解即可。

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