You buy furniture for $2,500. you pay $300 down and the retailer finances the remainder with 36 monthly payments of $80. calculate your apr.

The amount financed is $2500 -300 = $2200.

The APR is calculated using a financial calculator based on this amount, the monthly payment, and the number of months.

The APR for this financing is 18.42%.

_____
The annuity formula can be solved for any of the variables except interest rate. For that, you need some machine help.

___
The APR is computed as the interest rate that would apply for the payment you make and the loan proceeds. The payment you make is computed from the amount financed. Here, the financed amount and the loan proceeds are the same (2200). The APR is computed from that amount and the payments you agree to (80).

In other cases, there may be fees or points involved, so the amount financed will be higher than the proceeds of the loan. Then the APR is higher than the nominal rate used to calculate the payments.