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X · 2022年05月14日

为什么1875000是PV,而不是FV呢？

  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

FV是1875000不就代表是未来付清贷款的金额，然后PV等于0求PMT么？

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1 个答案

星星_品职助教 · 2022年05月14日

同学你好，

题干说明“... pay 25% of the full price now and the left money is financed at 10%”，所以这“left”的1,875,000是现在就要付的，也就是现在欠下的贷款金额。

如果FV=1,875,000，意思是在第25年末还欠这么多钱。而实际上，这个钱是现在欠下的，通过每年的PMT最后在第25年末还清的。由于第25年末贷款已经还清，所以FV是0.

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