Cassandra is repaying an installment loan of $3500 with 20 equal monthly payments of $196 each. What is the annual percentage rate of the loan?
If there are N payments of $M to pay off a principal of $P, let
q = log2(1+1/N) = log(1+1/N)/log(2)
then a good approximation for the interest rate per payment is given by
r = ((1+M/P)^(1/q) - 1)^q - 1
In our case,
q = 0.070389
1/q = 14.206699
M/P = .0056
r = 0.011029
annual interest rate is 12r = 13.23%