You have just purchased a car and, to fund the purchase, you borrowed $31,000. If your monthly payments are $493.25 for the next 6 years, what is the APR of the loan?

4.56%

Explanation:

The annual percentage rate refers to the rate at which the loan amount is equal to the present value of cash flows

In mathematically

Loan amount = Present value of cash flows

Loan amount = Monthly payment * PVAF (rate, number of years)

$31,000 = $493.25 * PVAF (rate, 72 months)

So,

PVAF (rate, 72 months) = 62.8485

And, the monthly rate is = 0.38%

So, the APR is

= Monthly rate * total number of months in a year

= 0.38% * 12

= 4.56%

The 72 months is

= 6 years * 12 months

= 72 months