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15 April, 14:16

Ethel and Jack each separately apply for and receive a loan worth $7,725 apiece. Ethel has a relatively average credit rating, so her loan has an APR of 9.14%, compounded monthly. Jack's credit rating is excellent, so his loan has an APR of 6.88%, compounded monthly. If they both pay off their respective loans by making six years of identical monthly payments, how much more will Ethel pay than Jack?

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  1. 15 April, 14:25
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    For Ethel:

    P = 7725

    r = 0.0914

    n = 6

    Converting nominal interest rate to effective annual interest rate

    i = (1 + 0.0914/12) ^12 - 1 = 0.0953

    Solving for the yearly payments:

    A = 7725 [0.0953 (1 + 0.0953) ^6] / [ (1 + 0.0953) ^6 - 1]

    A = $1,749.50

    For Jack:

    P = 7725

    r = 0.0688

    n = 6

    Converting nominal interest rate to effective annual interest rate

    i = (1 + 0.0688/12) ^12 - 1 = 0.0710

    Solving for the yearly payments:

    A = 7725 [0.0710 (1 + 0.0710) ^6] / [ (1 + 0.0710) ^6 - 1]

    A = $1,625.74

    Ethyl will pay

    $1,749.50 - $1,625.74 = $123.76 more than Jack
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