Question

A $209,000 mortgage for 30 years for a new home is obtained at the rate of 8,5% compounded monthly. Find (a) the monthly payment, (b) the interest in the first payment, (c) the principal repaid in the first payment, and (d) the finance charge. (a) The monthly payment on the mortgage is $ (Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed) (b) The interest in the first payment is (Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed) (c) The principal repaid in the first payment is (Round the final answer to two decimal places as needed. Round all intermediate values to six decimal places as needed) (d) The finance charge is (Round to two decimal places as needed.)

Answer 1

The equation to find monthly payments of a loan is

$\large Payment= \frac{r*P}{1-(1+r)^{-n}}$

here P is amount borrowed

r is rate of interest in decimal per month .if Apr is given ,then divide it by 1200 to get this.

$\large r=\frac{Apr}{1200}$

n is number of payments. If number of year is t ,then n=12t

For this mortgage P=209000

n= 30*12=360

interest rate Apr is 8.5% .so

$\large r=\frac{8.5}{1200}=0.007083$

apply these values to equation

$\large Payment=\frac{0.007083*209000}{1-(1+0.007083)^{-360}}=1606.97$

so monthly payments = 1606.97

b) equation to find interest in first payment is

interest in first payment = P*r= 209000*0.007083=1480.35

so answer is 1480.35

c) to get principle repaid in first payment subtract interest in first payment from monthly payments

principle repaid=1606.97-1480.35= 126.62

so answer is 126.62

d) to get finance charge (total interest) first find total amount paid.

total amount paid=1606.97*360=578509.2

so finance charge= total amount paid- amount borrowed = 578509.2-209000=369509.2

so answer is 369509.2