Question

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. a. 5.48% b. 8.43% c. 18.55% d. 15.65% please select the best answer from the choices provided a b c d

Answer 1

The percentage of the total finance charge will the service charge is 15.65%. Then the correct option is D.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

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.

A = $15360

r = 0.0958/2 = 0.0479

n = 8 × 2 = 16

The periodic payment is given as

$\rm A = P (\dfrac{1-(1+r)^{-n}}{r})$

Where P is Periodic payment

r = rate per period

n = number of period

Then we have

$\rm 15360 = P(\dfrac{1-(1+0.0479)^{-16}}{0.0479})\\\\\\ P = 1396.16$

Then Sam will pay a total of 1396.16 × 16 = $22,338.56

Interest charge = 22338.56 – 15360 = $6978.56

Total finance charge = 6978.56 + 1294.64 = $8273.20

Then the percentage of the total finance charge will the service charge will be

$\rm Percentage = \dfrac{1294.64}{8273.20}*100\\\\Percentage = 15.65 \%$

More about the percentage link is given below.

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