# math

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A car dealer will sell you a used car for \$7,742 with \$742 down and payments of \$309.93 per month for 24 months. What is the APR?

• math -

So your present value of the loan = \$7000
n = 24
i = ??
P = 309.93

7000 = 309.93(1 - (1+i)^-24)/i
solving this for i is very messy, and we have no algebraic formulas that will do that.
I set up an Excel program where I found
a montyly rate of .004915 to come withing a few pennies of \$7000
so the APR = 12(.004915) = .05898 or 5.898%

check: 309.93(1 - 1.004915^-24)/.004915 = 7000.17

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