Question

Kerri James is considering the purchase of a car, which will cost her $24,600. She will borrow the entire purchase price and make monthly payments over the next six years. The first payment is due next month and the annual interest rate is 3.00%. She will owe $____ on the car immediately following the 18th payment.

A. 18,858.19

B. 18,531.57

C. 20,757.33

D. 19,184.00

E. 23,258.56

Answer 1

Answer is $18,858.19

Cost of car = $24,600
Annual interest rate = 3.00%
Monthly interest rate = 0.25%
Time period = 6 years or 72 months

Let monthly payment be $x

$24,600 = $x/1.0025 + $x/1.0025^2 + ... + $x/1.0025^72
$24,600 = $x * (1 - (1/1.0025)^72) / 0.0025
$24,600 = $x * 65.816858
$x = $373.76

Monthly payment = $373.76

After 18th payment:

Remaining number of payments = 54

Loan outstanding = $373.76/1.0025 + $373.76/1.0025^2 + ... + $373.76/1.0025^54
Loan outstanding = $373.76 * (1 - (1/1.0025)^54) / 0.0025
Loan outstanding = $373.76 * 50.454753
Loan outstanding = $18,858.19

She will owe $18,858.19 on the car immediately following the 18th payment.