Question

Chapter 5 Connect Problems i Saved Help Save & Exit Submit Check my work 23 Rachel purchased a car for $20,000 three years ago using a 4-year loan with an interest rate of 9.0 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. points 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.) Skipped Minimum price eBook Ask Print References Me Graw < Prey 23 of 23 !!! Next >

Answer 1

Interest rate per months is (0.09/12) = 0.0075.

$Loan=Monthly\, payment\times \left ( \frac{1-\left ( 1+i \right )^{-n}}{i} \right )$

$20,000=Monthly\, payment\times \left ( \frac{1-\left ( 1+0.0075 \right )^{-48}}{0.0075} \right )$

$20,000=Monthly\, payment\times \left ( \frac{0.3013858641}{0.0075} \right )$

20,000 = Monthly payment x 40.18478189

497.70 = Monthly payment

The remaining balance on loan is:

$Loan\, balance=497.70\times \left ( \frac{1-1.0075^{-12}}{0.0075} \right )$

$Loan\, balance=497.70\times \left ( \frac{0.08576184505}{0.0075} \right )$

$Loan\, balance=497.70\times 11.43491267$

Minimum price is $5,691.16.