Question

Rachel purchased a car for $25,000 three years ago using a 4-year loan with an interest rate of 10.8 percent. 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. What is the minimum price Rachel would need to receive for her car? Calculate her monthly payments , then use those payments and the remaining time left to compute the present value (called balance) of the remaining loan. (Do not round Intermediate calculations and round your final answer to 2 decimal places .)

Answer 1

Cash price	$          25,000.00
Loan term	4 years
Interest rate	10.80%
Payment frequency	Monthly
Effective interest rate	((1+(10.8%/12))^12)-1)
Effective interest rate	11.35%
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream	25000
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	11.35%
i=nominal Interest rate	10.80%
n = the number of periods in which payments will be made	4
25000	= PMT *(((1-(1 + r) ^- n)) / i)
25000	= PMT *(((1-(1 + 11.35%) ^- 4)) / 10.80%)
25000	= PMT *3.2365
Monthly payment * 12=	25000/3.2365
Monthly payment * 12=	$            7,724.55
Monthly payment=	7724.55/12
Monthly payment=	$               643.71
PV of remaining 12 monthly installments will be the price required to sell the car
P = PMT x (((1-(1 + r) ^- n)) / i)
Required PV=	643.71*12 * (((1-(1 + 11.35%) ^- 1)) / 10.80%)
Required PV=	$            7,291.02
Minimum price required to sell the car=	$            7,291.02