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CY · 2021年04月24日

请问这一部分是求的什么？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000014

问题如下：

Grandparents are funding a newborn’s future university tuition costs, estimated at $50,000/year for four years, with the first payment due as a lump sum in 18 years. Assuming a 6% effective annual rate, the required deposit today is closest to:

选项：

A.

$60,699.

B.

$64,341.

C.

$68,201.

解释：

B is correct.

First, find the present value (PV) of an ordinary annuity in Year 17 that represents the tuition costs:  50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}  = $50,000 × 3.4651 = $173,255.28. Then, find the PV of the annuity in today’s dollars (where FV is future value):

PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}

PV0 = $64,340.85 ≈ $64,341.


可以请助教再详细解释一下解题逻辑嘛？谢谢！

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1 个答案

星星_品职助教 · 2021年04月24日

同学你好，

这种方式是试图用公式去解决货币时间价值问题。公式我们上课是不讲的。这种公式所有部分都不用看，货币时间价值问题我们统一都用计算器解决。

以本题的解题逻辑为例：

题目的意思相当于在T=18的时候开始交50,000这一笔钱，要交四年，所以要先对这四笔钱折现。具体如下图所示：

由图可知，这里的第一笔50,000发生在18年末19年初，“in 18 years”可以看出来，即在T=18时交第一笔钱，折现之后算出的PV其实是T=17时的PV。N=4; I/Y=6; FV=0; PMT=50,000; CPT PV=173255.28

因为题目要求的是今天应该存多少钱，然后再进行下一步折现，STEP 2: N=17; PMT=0; I/Y=6; FV=173255.28; CPT PV=64340.85，即本题的答案。

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NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41​​] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0​=(1+0.06)17FV​=(1+0.06)17173,255.28​PV0 = $64,340.85 ≈ $64,341. 173255.28我能算出来 但为什么下一步时间是17 不是18

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