Elliott purchased a used pick-up truck for $9,500 he put $500. as a down payment and will repay the balance in monthly payments of $365. over the next 3 years. what is the apr of this loan?

The question will be solved using the present value of annuity formula.

Now, since he made a down payment of $500, The amount left to be paid is given $9,500 - $500 = $9,000.

The present value of annuity is given by:



where: PV = $9,000; P = $365; t = 12 payments per year, n = 3 years; r = APR and



is the Present value of annuity factor for periods at interest rate per period.

Here, there are 3 years x 12 monthly payments = 36 periods.

Thus,



This means that the present value of annuity factor is 24.657534.

Using the present value of annuity table, the present value of annuity facot for 36 periods at 2% interest rate per period is 25.488842 and at 3% is 21.832253.

Let the interest rate that give the present value of annuity factor of 24.657534 be x, then interpolating, we have:

Let , then we have:



Thus, the interest rate per period (r/12) = 2.227345%.

Therefore, the APR = 12 x 2.227345 = 26.7281 ≈ 26.7%

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