Question

You have just finished paying off your $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? Round all dollar values to the nearest cent. A. 25. 69% b. 36. 47% c. 57. 41% d. 27. 10%.

Answer 1

The percentage of the total cost for the finance charges is 36.47%

Computation:

Given,

$P$ Principal amount= $35,125

$r$ Interest rate =7.44%

$t$ Compounding period = quarterly 4

$n$ Time period =10 years

The formula of the annuity will be used to determine the total cost:

$\begin{aligned}A&=P\times\dfrac{(1+\frac{r}{n})^{n-1}}{r\times(1+\frac{r}{n})^n}\\&=\ 35,125\times\dfrac{(1+\frac{0.0744}{10})^{10-1}}{0.0744\times(1+\frac{0.0744}{10})^{10}}\\&=\ 1,252.70\end{aligned}$

$\begin{aligned}\text{Total cost}&=A\times(n\times t)\\&=\ 1,252.70\times(10\times 4)\\&=\ 50,108\end{aligned}$

Now, the percentage of finance charges will be determined as follows:

$\begin{aligned}\text{\% of Finance Charges}&=\dfrac{\text{Total Cost+ Service Charges-Principal Amount}}{\text{Total Cost+ Service Charges}}\times100\\&=\dfrac{\ 50,108+\ 5,180.0-\ 35,125}{\ 50,108+\ 5,180.70}\times100\\&=36.47\%\end{aligned}$

Therefore, the percentage of finance charges is correct in option b. 36.47%.

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