posted by Sandy
Cassandra is repaying an installment loan of $3,500 with 20 equal monthly
payments of $196 each. what is the annual percentage rate of the loan?
The standard formula for installment amount A, for n periods with interest per period i, and present value (principal) P is
substitute to get
I do not believe there is an explicit formula to solve for i, so we can solve it by trial and error or by iteration.
Rearrange to give
and we look for i that makes f(i)=0.
Make a table:
Interpolating, we try
So give a final try of
The interest per period is 1.1045%