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vici · 2020年09月07日

问一道题：NO.PZ2017092702000014

  1. CFA I
  2. Quantitative

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.

问题：有关18岁支付学费使用的年金方法应该是先付你年金，还是后付年金。


截取“你第一步计算PV的方法并不是上课讲过的方法，也比较复杂。完全没有必要那么考虑，直接用上课讲过按计算器算PV即可。普通年金，N=4，PMT=50,000，I/Y=6， FV=0，CPT PV=-173255.28“


自己理解：

老师，这里学费都是每年年初支付的，所以我用BGN的计算器方法进行了

BGN--N=4，PMT=50,000，I/Y=6， FV=0，CPT  PV=183650.5974


麻烦解释一下，题目在这一步为何用了后付年金的方法？


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1 个答案

星星_品职助教 · 2020年09月07日

同学你好，

这个问题可以统计来记忆理解。无论是学费还是其他的情况，不需要由自己来判断是先付还是后付，需要根据题干信息来进行判断。如果是先付年金，题干会特意强调先付，如果题干什么都没说，那么自动按照后付来处理即可。

这道题其实不需要特意去考虑是什么年金的问题，题干告诉的是具体时间点。通过“with the first payment due as a lump sum in 18 years”可知，这句话的意思是首笔付款在N=18这个时间点进行，所以四笔现金流的时间点就是18,19,20,21，按照这个以后付年金的方式计算PV计算到N=17时间点即可。不需要调BGN模式

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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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2023-05-22 14:50 1 · 回答

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