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1 September, 11:56

Amber borrows $5,000 from the bank. If she repays the loan in 5 years, the annual interest rate is 8%, compounded annually. However, if she can repay the loan in 3 years, the annual rate is 6.5%, compounded annually. How much interest will Amber save by repaying the loan in 3 years? (to the nearest dollar) A) $1,152 B) $1,307 C) $583 D) $971

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  1. 1 September, 12:18
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    Option B is correct

    Amount amber will save = $1307

    Step-by-step explanation:

    The formula of the compound interest is

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

    If she repays a loan in 5 years

    P=$5000 (principle amount)

    r=8%=0.08 (interest rate)

    t=5 (no of years)

    n=1 (no of times per year interest is paid)

    A=5000 (1+0.08/1) ^ (1 (5))

    A=5000 (1.08) ^5

    A=5000 (1.4693)

    A=$7346.6403

    formula for interest amount is

    I=A-P

    I=$7346.6403-$5000

    I=$2346.64

    If she repays a loan in 3 years

    P=$5000 (principle amount)

    r=6.5%=0.065 (interest rate)

    t=3 (no of years)

    n=1 (no of times per year interest is paid)

    A=5000 (1+0.065/1) ^ (1 (3))

    A=5000 (1.065) ^3

    A=5000 (1.2079)

    A=$6039.7481

    formula for interest amount is

    I=A-P

    I=$6039.7481-$5000

    I=$1039.7481

    then To find the amount of interest that Amber will save by paying in 3 years we will subtract the amount of interest in 5 years with the amount of interest in 3 years

    Interest Amount that amber will save = $2346.64 - $1039.7481

    =$1306.8918

    That will be nearest to $1,307
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