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?
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.
To find the finance charge per $100 of the amount financed, we need to calculate the total finance charge and then divide it by the amount financed.
First, let's calculate the total finance charge:
Total Amount Repaid = Monthly Installment * Number of Installments
Total Amount Repaid = $232 * 12
Total Amount Repaid = $2,784
Finance Charge = Total Amount Repaid - Amount Borrowed
Finance Charge = $2,784 - $2,600
Finance Charge = $184
Now, let's calculate the finance charge per $100 of the amount financed:
Finance Charge per $100 = (Finance Charge / Amount Financed) * 100
Finance Charge per $100 = ($184 / $2,600) * 100
Finance Charge per $100 = 0.07 * 100
Finance Charge per $100 = 7
Therefore, the finance charge per $100 of the amount financed is $7.