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rabbit · 2020年09月17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.

老师，对于先付年金、后付年金，根据你们多年经验，题目有什么关键词以区分吗？我总是弄错。原以为出现DUE 、TODAY 就是先付年金的提示，但发现也没这个规律。

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2 个答案

星星_品职助教 · 2021年01月18日

@Baby 8 肖闲

同学你好，做题目根据题干的描述去解题即可。只要没有刻意的先付年金的提示，都默认为后付年金

如果之前做到协会出的题目，题干没有说是先付却最终用了先付，可以粘贴上来看一下。

星星_品职助教 · 2020年09月17日

同学你好，

有几个规律可以记忆一下：

1. 如果考先付年金，题干会有非常明显的提示；如果没有刻意的提示，都默认为后付年金，不需要自己去判断是什么年金。

2. 先付年金的关键词往往是pay...at the beginning of the year，或者是make the payment today。无论题干怎么描述，核心的含义都是在期初付PMT。与之对应的与pay...at the end of the year

3. 虽然先付年金名字叫做annuity due，但是实际题目中，往往不用这个词，关键词也不是due。而是通过直接描述在期初付款的方式来暗示需要用先付年金计算。例如本题，due就是正常的含义即到期到支付的意思，并不代表先付。

*Baby 8 肖闲* · 2021年01月18日

老师您好，关于支付学费，之前做题当中并没有提到说学费年初支付但也都是先付年金，所以我当时的理解就是学费就是先付，也是比较符合常理的，但看到您的解释是说即便是学费，如果题干中并没有说是先付，也是应该默认为后付，就是也不需要考虑生活中的常理理解这样是吗？

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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

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. N=18， I/Y= 6， PMT=0, FV = 200000 这样哪里错了

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