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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%

Respuesta :

15360 =  P {1-(1.0479)^-16 / 0.0479]

15360 /  {1-(1.0479)^-16 / 0.0479]  = P

P = 1396.1604

Sam's total payment = 1396.1604^16  = 22338.56
interest charge = 6978.56
Total finance charge = 8273.20

1294.64/8273.2 x 100 = 15.6486

I think the answer is D. 15.65 %

hope this helps

ajeigbeibraheem

The percentage of the total finance charges that the service charges is 15.65%

What are finance charges?

A finance charge is a fee that is applied to the usage of credits or the expansion of credit. It might be a one-time fee or a proportion of the amount borrowed, with percentage-based financing fees being the most frequent.

From the given information:

  • The future value Sam is paying back = $15,360
  • The interest rate on the loan = 9.58%/2 = 0.0479
  • The principal value = ??
  • Service charge = $1294.64
  • Time (t) = 16 (compounded semi-annually)

Since the future value is compounded semiannually; the principal value can be estimated by using the formula:

[tex]\mathbf{FV = P( \dfrac{1 - (1+r)^{(-t)}}{r})}}[/tex]

[tex]\mathbf{15360= P( \dfrac{1 -(1+0.0479)^{(-16)}}{0.0479})}}[/tex]

[tex]\mathbf{15360= P(11.0016)}[/tex]

P = 15360/11.0016

P = $1396.161

However,

  • The total amount Sam pays = $22338.56.
  • The interest charged on the amount paid =  $6978.56
  • Total finance charge = $8273.20

The percentage of the finance charge is computed as:

[tex]\mathbf{=\dfrac{1,294.64}{8273.20} \times 100 }[/tex]

= 15.65%

Learn more about Finance charges here:

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