开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

Sofia nice · 2023年05月21日

先付？后付？

  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.

老师，学费不是都应该先付吗？这个不按照常识处理吗？另外，如果，18时点开始的payment 是先付，是不是答案就是C啊？，折到17年初，也就是16年末是173255。

添加评论
1 个答案
已采纳答案

星星_品职助教 · 2023年05月21日

​同学你好，学费需要按照题干提示处理，如未提示先付（如本题），都需要按后付处理。本题中，“…first payment…in 18 years代表首笔付款位于18时点上，所以首次折现到17时间点，二次折现再折17期到0时点。

  • 1

    回答

  • 1

    关注

  • 300

    浏览
相关问题

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

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. 第一步， PMT=50000，N=4,I/Y=6，FV=0，算出PV，用算出的PV值再乘以（1+I/Y），这个就是后面要求的值的FV第二步，用上面最终求得的值作为FV，PMT=0，N=18，I/Y=6，求PV这里第二步的N是不是就应该用18来算？

2023-05-22 14:50 1 · 回答