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23 July, 06:29

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.

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  1. 23 July, 06:32
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    The total amount of interest Samantha will pay=$40,842.47

    Step-by-step 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
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