You have just purchased a car and, to fund the purchase, you borrowed $32,000. If your monthly payments are $615.13 for the next 5 years, what is the APR of the loan?

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  5.76%

Step-by-step explanation:

There is no formula for APR. It must be found using an iterative calculation, as from a spreadsheet or financial calculator.

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The value can also be found graphically from the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal amount of the loan, r is the annual rate, and t is the number of years.

This can be put into a form that can be solved easily by a graphing calculator. We want it to find the x-intercept of f(x) = 0, so we define ...

  f(x) = A(P, x/100, t) -615.13

where A(P, r, t) is defined above, and we let r = x/100 so x is the APR. The graph shows us the APR is 5.763%.

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