Wade Ellis buys a car for $17,224.93. He puts 10% down and obtains a simple interest amortized loan for the balance at 13 and 1/2% interest for four years. After three years and two months of making the minimum monthly payment, he sells his car. Find the unpaid balance on his loan. (Round all intermediate calculations to the nearest cent. Round the answer to the nearest cent.) $

You want the remaining balance on a 4-year loan at 13.5% for a $17,224.93 car after 10% is put down and payments are made for 3 years and 2 months.

Loan amount

The amount borrowed will be ...

$17,224.93 × (1 -10%) = $15,502.44

Payment

The payment on the loan will be ...

[tex]A=\dfrac{Pr}{12(1-(1+r/12)^{-n})}[/tex]

where P is the amount borrowed at annual rate r for n payments.

When $15,502.44 is borrowed at 13.5% with 48 payments scheduled, the payment amount is ...

[tex]A=\dfrac{15502.44(0.135)}{12(1-(1+0.135/12)^{-48})}\approx419.75[/tex]

Balance

The balance after n payments is ...

[tex]B=P(1+r/12)^n-12A\left(\dfrac{(1+r/12)^n-1}{r}\right)\\\\\\B=15502.44(1.01125)^{38}-12(419.75)\left(\dfrac{1.01125^{38}-1}{0.135}\right)\approx3949.00[/tex]

The unpaid balance after 38 payments is $3949.00.