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JanetS · 2023年10月04日

starting next year…

  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.

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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星星_品职助教 · 2023年10月06日

同学你好，

题干未说学费是先付年金。

所以，首笔学费在18时间点开始支付，求现值就不能折到18时间点本身，否则相当于期初付款的先付年金。

后付年金的首笔付款是第一期的期末，故首笔付款在18时间点意味着该后付年金折现应该折到17时间点。

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