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王二狗 · 2021年11月03日

你好，这道题可以理解成，因为18岁是due（先付/年初付），所以17岁就得把钱都存好吗？，所以求PV用的N是17

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.

你好，这道题可以理解成，因为18岁是due（先付/年初付），所以17岁就得把钱都存好吗？，所以求PV用的N是17

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星星_品职助教 · 2021年11月15日

@GS

1）题干中没有“annuity due”，只有正常应该直译的“due”；

2）直接按照后付方式计算即可，没必要用BGN模式去额外增加难度

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星星_品职助教 · 2021年11月15日

@GS

1）题干中没有“annuity due”，只有正常应该直译的“due”；

2）直接按照后付方式计算即可，没必要用BGN模式去额外增加难度

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星星_品职助教 · 2021年11月03日

同学你好，

1）“...with the first payment due as a lump sum in 18 years”指的是首笔现金流就在18这个时间点上发生。due直译为应付即可，并不代表先付年金。

2）根据题干可以确定四笔付款的时间点为18,19,20,21，所以计算此年金的现值是折现到第17时间点。所以第二步折现也是从17时间点折现回0时点，即第二步的N=17。

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GS · 2021年11月15日

1）“annuity due”不就是先付年金？ 2）用BGN把大学四年折现到18，第二步N=18？

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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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