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Amber · 2023年10月13日

本题细节不清楚

  1. Quantitative

NO.PZ2022123001000005

问题如下：

A couple plans to pay their child’s college tuition for 4 years starting 18 years from now. The current annual cost of college is C$7,000, and they expect this cost to rise at an annual rate of 5 percent. In their planning, they assume that they can earn 6% annually. How much must they put aside each year, starting next year, if they plan to make 17 equal payments?

选项：

A.$2,221.58 B.$2,300.78 C.$3,038.74

解释：

Step1: calculate the CF since 18,

CF18=7000*(1+5%)18 =16846, CF19=7000*(1+5%)19 =17689,…

Step 2: PV of tuition (4 CF since 18) at year 17

C$16,846 (1,06)-1 + C$17,689 (1.06)-2 + C$18,573 (1.06)-3 + C$19,502 (1.06 )-4 =$62,677

Step 3: Calculate PMT

Input FV=C$62,677, PV=0, I/Y=6, N=17, then CPT PMT= C$2,221.58

In summary, the couple will need to put aside C$2,221.58 each year if they start next year and make 17 equal payments.

两个问题

  1. 为什么四笔现金流折现到t17用的是6%不是5%作为折现率，怎么区分
  2. 这道题和基础班讲义的题有什么区别，为什么基础班的这题可以直接按计算器


谢谢老师

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1 个答案
已采纳答案

星星_品职助教 · 2023年10月15日

同学你好，

1）5%是学费的增长率。本题要折现的目的是求夫妻每年需要存入多少钱（PMT），所以需要用夫妻收入的增长率，而不是学费的。

2）例题的四笔学费是年金的形式，即每年金额不变，所以可以用计算器。本题学费每年增长5%，所以并不是等额现金流或年金，没法用年金的方法来计算。需要逐笔计算出金额后，再折现。

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NO.PZ2022123001000005问题如下 A couple plans to paytheir chils college tuitionfor 4 years starting 18 years from now. The current annucost of college isC$7,000, anthey expethis cost to rise annurate of 5 percent. In their planning, they assume ththey canearn 6% annually. How mumustthey put asi eayear, startingnext year, if they plto make 17 equpayments? A.$2,221.58B.$2,300.78C.$3,038.74 Step1: calculate the sin18,CF18=7000*(1+5%)18 =16846, CF19=7000*(1+5%)19 =17689,…Step 2: PV of tuition (4 sin18) ye17C$16,846 (1,06)-1 + C$17,689 (1.06)-2 + C$18,573 (1.06)-3 + C$19,502 (1.06 )-4 =$62,677Step 3: Calculate PMTInput FV=C$62,677, PV=0, I/Y=6, N=17, then CPT PMT= C$2,221.58In summary, the couple will neeto put asi C$2,221.58 eayeif they start next yeanmake 17 equpayments. 题干里说明年开始支付一直到第18年，一共支付17年。支付完最后一笔PMT应该刚好到了第18年。所以学费应该从第18年开始而不是第17年，为什么答案里4年学费还要折现到第17年而不是折现到第18年？

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