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荣 · 2020年05月26日

问一道题：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: $50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}$ = $50,000 × 3.4651 = $173,255.28. Then, find the PV of the annuity in today’s dollars (where FV is future value):

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

PV0 = $64,340.85 ≈ $64,341.

这道题用两次先付年金算出为答案C,用两次后付年金算出答案B，为什么不能用先付，付学费不是在18年的年初付的吗？

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星星_品职助教 · 2020年05月26日

同学你好，

这道题的关键点在于“the first payment due as a lump sum in 18 years”，这句话指的是第一笔付款在T=18这个时间点上付，从而可以得出四笔大学的付款时间分别是T=18,19,20,21，然后计算年金现值即可，用后付年金是因为比较简单。直接算到17时间点就可以了。也可以用先付年金算到T=18时间点，但是没有必要。

第二次折现就是把刚刚计算出来的现值从T=17折现回T=0，这是已知FV求PV的问题，不涉及年金。

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王思祺 · 2020年08月13日

老师能画个图吗，为什么我觉得n应该等于18呢？18年末的fv折回到0时刻不应该是18吗

星星_品职助教 · 2020年08月13日

@王思祺看到你在另一个问题下的回复了，加油~

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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)17173,255.28PV0 = $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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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