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

Answer 1

Percentage of finance charge as service charge= 15.6%

Step-by-step explanation:

Monthly installment = Loan amount /annuity factor

Annuity factor = (1- (1+r)^(-n))/r

r - semi-annul interest rate = 9.58%/2

n= number of period : 2×8 = 16

Annuity factor =( 1- (1.0479))^(-16)/0.0479

=11.0016

Monthly installment = 15,360 /11.00

=$1396.160

TotaL amount paid = 1396.160459× 16 =22,338.56

Interest charges = 22,338.56 - 15,360

= $6978.56

Percentage of total finance charge as service charge=

=1294.64/(1294.64+6978.567348)× 100

= 15.6%

Answer 2

15.65%

Step-by-step explanation:

we must determine the payment using the annuity formula:

present value = payment x {1 - (1 + r)⁻ⁿ / r]

• present value = 15,360
• r = 9.58% / 2 = 4.79%
• n = 8 x 2 = 16

15,360 = payment x {1 - (1 + 0.0479)⁻¹⁶ / 0.0479]

payment = 15,360 / {1 - 1.0479⁻¹⁶ / 0.0479] = 1,396.16

total payments = 1,396.16 x 16 = $22,338.56

interest charge = $22,338.56 - $15,360 = $6,978.56

total finance charge = $6,978.56 + $1,294.64 = $8,273.20

$1,294.64 / $8,273.20 = 0.1565 or 15.65%