Question

Rachel purchased a car for $22,500 three years ago using a 4-year loan with an interest rate of 7.2 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.)

Minimum price= _________________

Answer 1

Loan Balance (P) is =   22500  
interest rate =   7.2%  
Monthly rate (i)= 7.2%/12 =   0.006  
Number of months (n)=4*12=   48  
Monthly payment formula = P*i/(1-((1+i)^-n))      
22500*0.006/(1-((1+0.006)^-48))      
$540.88      
      
Remaining payment months after 3 years = 12*1=   12  
      
Unpaid balance (present value) formula (P)=monthly payment *(1-((1+i)^-n))/i      
540.88*(1-((1+0.006)^-12))/0.006      
$6,244.36      
So Loan balance is   $6,244.36  
      
So the minimum price Rachel would need to receive for her car is   $6,244.36