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Viola · 2021年10月30日

为什么这里第二步算PV的时候 N=17而不是18呢

  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.

为什么这里第二步算PV的时候 N=17而不是18呢

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星星_品职助教 · 2021年10月30日

同学你好，

根据“ the first payment due as a lump sum in 18 years”可知首笔付款是在18时间点的。所以第一步折现时，现值是算到第17时间点的。

这就和正常的后付年金现金流从1时间点开始，但折现是折到0时间点是一样的。

所以第二步就是从N=17而不是18开始折现了。

欢欢 · 2021年11月18日

第二步求的是先付年金的PV吗？看题干是“the required deposit today”。如果是的话，我用计算器直接算后付的然后再乘以（1+r），计算器是用N=17+1=18吗？因为除了T1到T17，按照后付的算法的话T0也是会有笔deposit吧？

星星_品职助教 · 2021年11月18日

@欢欢

所有的现值都是在0时点也就是“today”发生的，无论先付还是后付年金均是如此。

第二步折现中只有一笔FV，没有PMT，所以不需要去区分先付还是后付年金（差别在PMT发生时点不同）。无论此时是BGN模式还是END模式，FV=-173,255.2806，PMT=0，N=17，I/Y=6，CPT PV=64,340.8466这个结果都不会有差别。

星星_品职助教 · 2021年10月31日

@X｜

货币时间价值问题我们统一用计算器第三排五个键来解题，不用公式来解（上课也没讲公式）。

本题第一步折现的计算器按法为PMT=50,000，N=4，I/Y=6，FV=0，CPT PV=-173,255.2806，这是在N=17时间点的PV。

第二步再把这个值折现回0时点计算PV，此刻这个值就是17时间点的FV了。计算器按法为FV=-173,255.2806，PMT=0，N=17，I/Y=6，CPT PV=64,340.8466

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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

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. N=18， I/Y= 6， PMT=0, FV = 200000 这样哪里错了

2023-09-19 22:24 1 · 回答

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2023-08-21 16:57 1 · 回答

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2023-05-22 14:50 1 · 回答

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2023-05-21 17:37 1 · 回答