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paige · 2020年03月09日

问一道题：NO.PZ2017092702000014 [ CFA I ]

  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.

为什么在计算PV0的时候 N=17而不是18？题干不是说 a lump sum in 18 years么？
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1 个答案

星星_品职助教 · 2020年03月09日

同学你好，

a lump sum in 18 years指的是首笔payment在t=18时间点支付，四笔学费的时间点分别是18,19,20,21。这是一个年金的形式，算现值折现是折到17时点的。

可以理解为一个PMT在1,2,3,4,的年金，折现不是折到1时点，而是折到0时点的。

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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

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.first payment e，这里的e不是先付吗？如果不是，那么 题干一般如何表达先付呢？

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