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六姑娘 · 2023年06月30日

不太理解ARM最后那三步是什么意思,可以通过画图解释一下吗?

NO.PZ2022123001000006

问题如下:

A borrower is considering three competing mortgage loan offers from her bank. The amount borrowed on the mortgage is $100,000 with monthly compounding.


The rate on the ARM resets at the end of the year 3. Assuming the ARM is reset at 5.5% (i.e. the remaining balance on the loan will now be repaid with 5.5% nominal annual interest), which of the three loans will have the smallest monthly payment after the rate reset at the end of year 3?

选项:

A.30-year ARM B.15-year fixed-rate loan C.

30-year fixed-rate loan.

解释:

After year 3 the 30-year fixed-rate loan has the lowest payment. The loan payments, summarized in the table, are calculated using a financial calculator following the table.


Payment on the 30-year fixed is:

N = 12×30= 360; I/Y= (5/12) = 0.41667; PV= -100,000; FV = 0; calculate PMT=536.82

Payment on the 15-year fixed is:

N = 12×15= 180: I/Y= (4.385/12) = 0.36542; PV =-100,000; FV=0; calculate PMT=759.13

Calculations for the ARM

Initial payment

N = 12×30 = 360; I/Y = (3.75 / 12) = 0.31250; PV = -100,000; FV = 0; calculate PMT = 463.12

Balance at end of year 3:

N = 12×27 = 324; I/Y = (3.75 / 12) = 0.31250; FV = 0; PMT = 463.12; calculate PV = 94,270.54

Payment after the end of year 3:

N = 324; I/Y = (5.5 / 12) = 0.45833; PV = 94,270.54; FV = 0; calculate PMT = 559.15

不太理解ARM最后那三步是什么意思,可以通过画图解释一下吗?

1 个答案

星星_品职助教 · 2023年07月03日

同学你好,

第一步,当N为最开始的30年或360个月,I/Y仍为3.75 / 12时,计算出此时PMT为463.12

第二步,按照I/Y为3.75 / 12这个老利率,和上一步算出来的PMT=463.12。过了三年后,还剩27年或324个月,算出此时尚未还清的钱还有94,270.54

第三步,此时I/Y变为5.5/12,还剩上一步算出来的94,270.54没还,要是在未来的324个月中以这个新利率还完这么多钱,解出需要的新PMT是559.15.

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