Question

You borrow $2,600 and repay the loan in 12 monthly installments of $232.

What was the finance charge per $100 of the amount financed?

Answer 1

let the monthly interest rate be i
232( 1 - (1+i)^-12)/i = 2600
(1 - (1+i)^-12 )/i = 11.2069
1 - (1+i)^-12 = 11.2069 i
1 - (1+i)^-12 - 11.2069 i = 0

This equation cannot be solved by the usual standard methods.
we can try some values of i
let i = .01
LS = .0004818 , RS = 0 , not a bad guess

let i = .011
LS = -.000249 , hey that's even closer, but now it is negative,
So i must be between .01 and .011
do you get the idea?

correct to 5 decimals I got i = .01068

so the monthly charge on $100 is $1.068

Unusual way to state the question, usually it would be stated as an annual interest rate with the stated compound interest period

e.g. in this case:
.01068(12) or 12.816 % interest per annum compounded monthly.