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March 27, 2017

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Cassandra is repaying an installment loan of $3500 with 20 equal monthly payments of $196 each. What is the annual percentage rate of the loan?

  • Business Finance - ,

    If there are N payments of $M to pay off a principal of $P, let

    q = log2(1+1/N) = log(1+1/N)/log(2)

    then a good approximation for the interest rate per payment is given by

    r = ((1+M/P)^(1/q) - 1)^q - 1

    In our case,
    q = 0.070389
    1/q = 14.206699
    M/P = .0056

    r = 0.011029

    annual interest rate is 12r = 13.23%

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