Question

Paul has an eight-year loan with a principal of $26,900. The loan has an interest rate of 8.18%, compounded quarterly. If Paul pays $1,527 in service charges and makes quarterly payments on his loan, what will his total finance charge be when the loan is repaid? Round all dollar values to the nearest cent. a.$10,588.28 b.$11,546.36 c.$11,370.04 d.$1,527.00 Please select the best answer from the choices provided A B C D Mark this and return

Answer 1

Answer:

The answer is "option b"

Step-by-step explanation:

Amount = $26,900

r= 0.0818 %

$i=\frac{r}{4}$

 $=\frac{0.0818}{4}\\\\=0.02045$

t= 8 years

$n= 8 \times 4$

  $=32$

$D=\frac{1-(1+i)^{-n}}{i}$

   $=\frac{1-(1+0.02045)^{-32}}{0.02045}\\\\=\frac{1-(1.02045)^{-32}}{0.02045}\\\\=\frac{1-0.52319627}{0.02045}\\\\=\frac{0.47680373}{0.02045}\\\\=23.3155858$

$Q= \frac{Amount}{Discount \ factor }$

   $=\frac{26900}{23.3155858} \\\\=1153.73468$

Payment $=1153.73468 \times 32$

               $= \ 36919.5098$

$\text{Total interest = Payment - amount}$

                    $= \ 36919.5098 - \ 26900 \\\\ = \ 10019.5098$

$\text{Finance charge = Total interest + service charge}$

                        $= \ 10019.5098 + \ 1527\\\\ = \ 11546.5098$