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jvniki · 2022年12月15日

这题 也是 根据FV PV I/Y PMT N 中的任何四个，求另一个

  1. CFA I
  2. Quantitative

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[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.

有点迷惑的是 FV 和PV 那个应该是0；

我的值好像不对 FV= 20w；pv = 0 ; I/Y =66%,N =17 求PMT.

看了答案对比，但有感觉额不太对

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已采纳答案

星星_品职助教 · 2022年12月16日

同学你好，

1）本题要计算的是“the required deposit today”，所以是计算PV的题目，计算器中显然不能将PV设置为0；

2）本题理解思路如下：

根据“ the first payment due as a lump sum in 18 years”可知首笔付款是在18时间点的。画在图像上，学费的四笔现金流就是右侧的四个蓝色箭头。

根据这四笔现金流的模式，将这四笔现金流统一折现到17时间点。这就和正常的后付年金现金流从1时间点开始，但折现是折到0时间点是一样的。

这个步骤的计算器按法为：

PMT=50,000，N=4，I/Y=6，FV=0，CPT PV=-173,255.2806。要注意这是在N=17时间点的PV。

第二步再把这个值折现回0时点计算PV，此刻-173,255.2806这个值就是17时间点的FV了。计算器按法为FV=-173,255.2806，PMT=0，N=17，I/Y=6，CPT PV=64,340.8466

jvniki · 2022年12月17日

这题我又重新做了一遍，我是看了您前几行的提醒 我又按照自己的思路做了下，结果对。但反过来看我和老师的解题思路不太一样。我是把18年后的大学学费，当成先付年金，得到18年的pv= 183,650.60;然后也是向前折，但是我不知道我折到的哪一年，我是用pv/(1+6%)^18 次方 算到了最终答案。我想问， 1，我这个思路对吗 2，我第二次是折到了0时刻 还是1时刻，我咋看呢，现在有些蒙的成分。

星星_品职助教 · 2022年12月20日

@jvniki

1）这个思路是可以解出本题答案的，但并不是解题的常规思路，有的题型也不适用。

2）常规思路是从现金流的角度出发，即给出18,19,20,21这四笔确定的现金流位置，那么就按照普通后付年金折到17时点。这种方法适用于所有的题目；

3）只要是求最终的现值，都是折现到0时点的，没有折现到1时点的情况。

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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