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Eliza · 2022年03月24日

为什么第二步N是17，而不是18呢？

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.

“with the first payment due as a lump sum in 18 years”这句的意思不是“用18年凑够了这些学费，并且第一次开始交是一次性交”嘛。所以不应该算出FV=17325.88后，理解为N=18,1/Y=6%,PMT=0,然后求直接用计算器求PV嘛。

（如果老师可以用画图说明一下就更好啦~谢谢！）

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星星_品职助教 · 2022年03月24日

同学你好，

“ the first payment due as a lump sum in 18 years”的理解应为：首笔付款就在18时间点。其中lump sum指的是首笔付款一次性支付，不再进一步分期支付。这个条件没什么用，从来没有出现过PMT还不是lump sum支付的情况。

有用的条件是由此可以得出四笔学费的现金流分别发生在18,19,20,21四个时点，所以此时对这个四期年金折现时，需要折现到17而非18时间点。

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。

所以第二步折现时就应该把17173,255.28从17时间点折回0时点，即FV=-173,255.2806，PMT=0，N=17，I/Y=6，CPT PV=64,340.8466

可参考如下的时间轴：

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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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