Question

You borrow $210,000 to purchase a home. the terms of the loan call for monthly payments over 30 years at a mortgage rate of 4.50 percent. what percentage of your first 60 months' total payments go toward interest?
a. 82 percent
b. 71 percent
c. 66 percent
d. 59 percent

Answer 1

First step, find the monthly payments.
Borrowed amount, P = 210000
Monthly interest, i = 0.045/12
Number of periods, n = 30*12=360

Monthly payment
$A=\frac{P(i*(1+i)^n)}{(1+i)^n-1}$
$=\frac{210000(0.045/12*(1+0.045/12)^360)}{(1+0.045/12)^360-1}$
$=1064.0392$    [to the 1/100 of a cent]


2. Calculate interest accumulated over 60 months
$I=210000((1+0.045/12)^{60}-1)$
$=52877.12$

3. Calculate value of payments
$F=\frac{A((1+i)^n-1)}{i}$
$=\frac{1064.039150634359((1+0.045/12)^{60}-1)}{0.045/12}$
$=71445.50$    to the nearest cent

4. Calculate percentage of interest paid
A. as a fraction of future values
Percentage of interest
=52877.12/71445.50
=74.01%
As a fraction of total amounts paid
Percentage of interest
=52877.12/(60*1064.0392)
=52877.12/63842.35
=82.82%