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29 March, 06:01

Davis is buying a new car for $21,349.00. He plans to make a down payment of $3,000.00. If he's to make monthly payments of $352 for the next 5 years what APR had he paid

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  1. 29 March, 09:51
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    He actually borrowed P=21349-3000=18349 (present value)

    Assume the monthly interest is i.

    then future value due to loan:

    F1=P (1+i) ^n=18349 (1+i) ^ (5*12) = 18349 (1+i) ^60

    future value from monthly payment of A=352

    F2=A ((1+i) ^n-1) / i=352 ((1+i) ^60-1) / i

    Since F1=F2 for the same loan, we have

    18349 (1+i) ^60=352 ((1+i) ^60-1) / i

    Simplify notation by defining R=1+i, then

    18349 (R^60) - 352 (R^60-1) / (R-1) = 0

    Simplify further by multiplication by (R-1)

    f (R) = 18349*R^60 * (R-1) - 352 (R^60-1) = 0

    Solve for R by trial and error, or by iteration to get R=1.004732

    The APR is therefore

    12 * (1.004732-1) = 0.056784, or 5.678% approx.
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