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婉婷 · 2022年06月05日

这个题为什么不需要将利率转化为EAR呢

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

这个题为什么不需要将利率转化为EAR呢

1 个答案

袁园_品职助教 · 2022年06月06日

嗨,爱思考的PZer你好:


有效年利率(effective annual return)是一种计算投资产品年度复合收益的方法。即在本期收益基础上将利息计入本金再投资的年度收益率,它是考虑了复利因素的收益概念。

这道题如果用EAR算,就比较麻烦。

  1. 你先求出EAR(1+10%/12)的12次方-1=10.47%。
  2. EAR是每年的复合收益,然后按照25年,算出PMT,我按了计算器,这个等于214093.78。
  3. 这个PMT是1年的PMT,由于货币时间价值的存在,是不能直接除以12转化为月PMT的,而是需要重新用一排5个键计算一遍,FV=214093.78,N=12,PV=0,I/Y=10/12,CPT PMT=-17038.1298。

这样还不如直接将N转换为月份,直接按计算器,得到每月的PMT来的快。


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