Rachel purchased a car for $17,500 three years ago using a 4-year loan with an i
ID: 2816258 • Letter: R
Question
Rachel purchased a car for $17,500 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.)Explanation / Answer
Cost of Car = $17,500
Annual Interest Rate = 10.80%
Monthly Interest Rate = 0.90%
Period = 4 years or 48 months
Monthly Payment * PVIFA(0.90%, 48) = $17,500
Monthly Payment * (1 - (1/1.009)^48) / 0.009 = $17,500
Monthly Payment * 38.83721 = $17,500
Monthly Payment = $450.60
Remaining Period of Loan = 1 year or 12 months
Loan Outstanding = $450.60 * PVIFA(0.90%, 12)
Loan Outstanding = $450.60 * (1 - (1/1.009)^12) / 0.009
Loan Outstanding = $450.60 * 11.32652
Loan Outstanding = $5,103.73
So, Rachel would need to receive a minimum price of $5,103.73 for her car
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