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Katherine · 2023年04月08日

换一个思路行不行

  1. CFA I
  2. Quantitative

NO.PZ2015120604000015

问题如下：

An investor is looking at a house worth $ 2.5 million. If he want to buy the house, he must pay 25% of the full price now and the left money is financed at 10%，compounded monthly over the next 25 years, Calculate the monthly mortgage payment in this case.

选项：

A.

$17,850

B.

$22,607

C.

$17,038

解释：

C is correct.

N = 25 × 12 = 300;

I/Y = 10 / 12;

PV = -2,500,000(1 - 0.25) = -1,875,000 (75% of the full price left);

FV = 0;

CPT PMT = $17038

N=300，利率0.83不变，PV是625000（首付），FV为2500000，然后求PMT，这个思路就是当下我先付625000然后每个月付多少钱能满足25年后用付了2500000，求PMT

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2 个答案

星星_品职助教 · 2023年04月12日

@Katherine

1）FV是期末发生的一次性现金流，无论站在谁的角度，期末都没有这一笔独立现金流发生，所以FV必然是0；

2）首付是投资者的自有资金，这笔钱不需要偿还，也不会产生“monthly mortgage payment”。只需要考虑从银行借的部分，也就是剩下的75%的钱。

星星_品职助教 · 2023年04月09日

​​同学你好， 1）本题计算的是“the left money”也就是剩余的钱应该怎么还？不需要考虑已经付了的首付，只需要考虑剩余的借了银行的钱。2）这笔钱是每期等额偿还的，并不是在期末一次性偿还了，所以期末的FV一定是0。FV=2500000相当于期末一次性还了2500000，与题干不符。

Katherine · 2023年04月10日

1，答案给的思路是站在投资者的角度，FV是0，如果站在银行的角度，FV就可以是250000吧，2，题目只是说剩下的钱会以百分之10的利率换，也没有说是只算剩下的钱部分啊

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