Question

Samantha is looking to determine the amount of interest that she will pay on her 4.7% , $40,000 loan over its 15 -year term. The loan compounds the interest monthly. Calculate the total amount of interest Samantha will pay, rounding to the nearest cent.

Answer 1

The total amount of interest Samantha will pay=$40,842.47

Explanation:

Step 1: Determine expression of total interest amount to be payed

The expression for the total interest amount to be payed inclusive of interest is given by;

A=P(1+r/n)^(nt)-P

where;

A=total amount of interest to be payed

P=principal loan amount

r=annual interest rate

n=number of compounding periods in a year

t=number of years

In our case;

P=$40,000

r=4.7%=4.7/100=0.047

n=12

t=15 years

replacing;

A=40,000(1+0.047/12)^(12×15)-40,000

A=40,000(1.00392)^180-40,000

A=40,842.46821

The amount rounded of to the nearest cents=1/100=0.01, round off to the nearest 2 decimal places=40,842.47

The total amount of interest Samantha will pay=$40,842.47