Payments of $27.50 are made monthly for a period of 36 months, and the amount financed is $835. What is the APR using the formula above?

The monthly payment for loans with no fees is expressed by a formula. The monthly payment equation is expressed as:

P = (P° x r x (1+r) ^N) / ((1+r) ^N - 1)

where P is the monthly payment, P° is the loan amount, r is the APR, N is the number of monthly payments

We substitute the values and manipulate where one side contains the unknown term r.

27.50/835 = (r x (1+r) ^36) / ((1+r) ^36 - 1)

Using some functions in the calculator we obtain,

r = 9.51 x 10^-3

Thus, the problem above has an APR of 0.95% monthly.