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holicess · 2021年11月13日

第一步可以用BGN 算么？

  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.

FV=0; I/R=6; PMT=50000; N=4; PV=?

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1 个答案

星星_品职助教 · 2021年11月14日

同学你好，

可以。

BGN模式的第一步折现，FV=0; I/Y=6; PMT=50,000; N=4; CPT PV= -183,650.5975, 此时这个PV在第18时间点。

第二步变成从18时间点折现回0时点，FV=-183,650.5975，PMT=0，N=18，I/Y=6，CPT PV=64,340.8466.

这种折现模式在第一步增加了没有必要的复杂性。了解即可，原版书上所有的两步折现问题第一步都是按照后付年金来处理的。

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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

2023-09-23 20:31 1 · 回答

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