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cui1130 · 2022年03月17日

如题

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[11(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.

为什么我算出来没有正确答案啊?

第一步:N=4,I/Y=6,PMT=-50000,FV=0,得到PV=173255

第二步:N=17,I/Y=6,PV=0,FV=173255,得到PMT=-6140.99

哪里错了呢?

2 个答案

星星_品职助教 · 2022年04月03日

@chuziyang

tuition fee并不能等同于先付年金,具体形式需要看题干条件。

本题题干并未有先付年金的提示,所以正常按照END模式计算即可。

星星_品职助教 · 2022年03月17日

同学你好,

第一步没有问题。第二步有错误。

这道题最终的目的是要求PV的。题干描述为the required deposit today is....所以,求的是“today”的唯一一笔现金流即PV。

这一步并没有每期的PMT,所以PMT应该为0.

如上所述,第二步最终正确的计算器按法应为:FV=-173,255.2806,PMT=0,N=17,I/Y=6,CPT PV=64,340.8466

chuziyang · 2022年04月03日

既然是tuition fee,請問第一步,計算器是否應該在BGN模式下計算?

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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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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