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$35,125 loan, a feat which took ten years of quarterly payments. The loan had an interest rate of 7.44%, compounded quarterly. If you also paid $5,180.70 in service charges, what percentage of the total cost was made up by your finance charges?

Verified Answer :

wizard123

First find the amount of each payment:
\(35,125 = P(\frac{(1+i)^{40} -1}{i (1+i)^{40}}) , i = \frac{.0744}{4} \\ \\ P = 1252.70\)

The total cost will be 40 payments plus service charges.
\(40*1252.70 + 5180.70 = 55,288.90\)

The percentage is the service charge divided by total cost:
\(X = \frac{5180.70}{ 55,288.90} = .0937 = 9.37\%\)