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Captain America · 2022年09月01日

请讲一下时间线

  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.

一个孩子如果第六年初（第五年末）交6000，那后付计算器算出来的PV不是第四年末的PV21275.7吗？为什么是第五年末呢？

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1 个答案

星星_品职助教 · 2022年09月01日

同学你好，

这道题不涉及第四、五、六年。时间轴上的两个重要时点是①“at 12 years old”，即12时点；和②“Six years later”，即12+6=18时点。这也是付首笔学费的时点。

根据以上条件可知，学费的四笔现金流时间固定为了18,19,20,21.所以此时的常规处理方式为首先将这四笔现金流折现到17时点。在往回折现5期折到12时点。这也是答案解析的思路，所有这类学费的题目都可以按照上述解题思路来解。


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另一个方法是将这四笔现金流折现到18时点，然后再往回折现6期折到12时点，结果是一样的。这种方法比较容易出错，不建议这样去解题。

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