Question

Rachel purchased a car for $23,500 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

It should sale the car for at least 6.853,55‬ to pay up the loan

Step-by-step explanation:

We need to calculate the balance of the loan after 3-years

Montly payment:

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV 23,500

time 48

rate 0.009

`23500 / (1-(1+0.009)^(-48) )/(0.009) = C\\`

C $ 605.090

interest:

23,500 x 0.009 = 211.50

amortization on first period:

605.09 - 211.5 = 393.59

Amortization after three years: future value of an annuity of the first amortization

`C * ((1+r)^(time) -1)/(rate) = FV\\`

C 393.59

time 36

rate 0.009

`393.59 * ((1+0.009)^(36) -1)/(0.009) = FV\\`

FV $16,646.4462

Balance: 23,500 - 16,646.45 = 6.853,55‬