Question

Rachel purchased a $17,500 car three years ago using a 10 percent, 6-year loan. She has decided that she would sell the car now, if she could get a price that would pay off the balance of her loan. First calculate her monthly payments, then use those payments and the remaining time left to compute the present value (called balance) of the remaining loan. What is the minimum price Rachel would need to receive for her car? (Round the loan payment to the nearest cent, but do not round any other interim calculations. Round your final answer to 2 decimal places.)

Answer 1

Using financial calculator BA II Plus - Input details:	#
I/Y = Rate/Frequency =	0.833333
FV = Future value =	$0
N = Total payment term x Frequency =	72
PV = Present value of Loan =	-$17,500.00
CPT > PMT = Payment =	$324.202161 or $324.20
Alternate formula-based method:
PMT = Payment = |PV| x R% x (1+R%)^N / ((1+R%)^N - 1)	$324.20

Formula for calculating outstanding balance:

R = 10%/12 ; n = 36 months = 36

FV = (PV*(1+R)^n)-(PMT*((1+R)^n-1)/R)

FV =(17500*(1+10%/12)^36)-(324.202161*((1+10%/12)^36-1)/(10%/12))

FV of loan or Outstanding loan = $10,047.43

She should receive $10,047.43 to pay off her loan balance.