Sam is paying off his eight-year, $15,360 loan in semiannual installments. The loan has an interest rate of 9.58%, compounded semiannually, and a service charge of $1,294.64. Once the loan has been fully paid off, what percentage of the total finance charge will the service charge be? Round all dollar values to the nearest cent.
+118658 I am assuming that the service charge of $1294.64 is paid up front and seperate to the rest of the loan.
I have made a few assumptions here. 
A=15360
r=0.0958/2 = 0.0479
n=8*2=16
$$\begin{array}{rll}
15360&=&P\left[\frac{1-(1.0479)^{-16}}{0.0479}\right]\\\\
15360\div \left[\frac{1-(1.0479)^{-16}}{0.0479}\right] &=&P\\\\
\end{array}$$
$${\frac{{\mathtt{15\,360}}}{\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{1.047\: \!9}}}^{-{\mathtt{16}}}\right)}{{\mathtt{0.047\: \!9}}}}\right)}} = {\mathtt{1\,396.160\: \!459\: \!256\: \!217\: \!018\: \!8}}$$
So Sam will pay a total of 1396.16*16 = $22338.56
Interest charged = 22338.56-15360 = $6978.56
Total finance charge = 6978.56+1294.64 = $8273.20
% wanted if I understand the terms correctly is 1294.64/8273.20*100
$${\frac{{\mathtt{1\,294.64}}}{{\mathtt{8\,273.2}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{15.648\: \!600\: \!299\: \!763\: \!090\: \!5}}$$
15.65%
