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为了求职冲呀 · 2020年05月04日

问一道题：NO.PZ2018062016000014

  1. CFA I
  2. Quantitative

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.

老师您好我看到其他同学的提问，菲菲助教解惑的图以及本题的答案。这道题目与课件19页的Annuity例题2相似，但何老师教的解题方式一样，但是为什么何老师解答时用的是END mode但是菲菲助教和题目把求FV6 用的是BGN mode呢？

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1 个答案

星星_品职助教 · 2020年05月06日

同学你好，

用哪种模式其实无所谓，只要现金流的时间确定好就行。以本题为例，四笔学费发生的时间就是6,7,8,9。

1) 如果采用后付年金的模式，就是折算到5时间点。

END 模式：N=4, I/Y=5, PMT=12,000, FV=0, CPT PV=-42,551.41，然后再把5时间点的44678.98折现到0时间点。FV=42,551.41，I/Y=5，PMT=0，N=5，CPT PV=-33,340.14

2) 如果采用先付年金的模式，则是折算到6时间点。

 BGN模式：N=4, I/Y=5, PMT=12,000, FV=0, CPT PV=-44,678.98。然后再把6时间点的44678.98折现到0时间点。FV=44,678.98，I/Y=5，PMT=0，N=6，CPT PV=-33,340.14

先付还是后付年金只是算法不同，影响的是第二步折现的N取多少，但是不会影响最终的结果。

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