On September 1, 2009, Susan Chao bought a motorcycle for $40,000. She paid $1,10

Question

On September 1, 2009, Susan Chao bought a motorcycle for $40,000. She paid $1,100 down and financed the balance with a five-year loan at a stated annual interest rate of 8.2 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2009). Two years later, at the end of October 2011, Susan got a new job and decided to pay off the loan.

If the bank charges her a 1 percent prepayment penalty based on the loan balance, how much must she pay the bank on November 1, 2011? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

  Total payment

$

On September 1, 2009, Susan Chao bought a motorcycle for $40,000. She paid $1,100 down and financed the balance with a five-year loan at a stated annual interest rate of 8.2 percent, compounded monthly. She started the monthly payments exactly one month after the purchase (i.e., October 1, 2009). Two years later, at the end of October 2011, Susan got a new job and decided to pay off the loan.

Explanation / Answer

Montly interest rate = 8.2/12 = 0.683%

Amount of loan = 40000 - 1100 = $38900

Monthly repayment = 38900/ (5*12) = $648.33

Remaining Balance = PV (1+r)n - P [{(1+r)n - 1}/r]

                                 = 38900 (1+0.00683)60 - 648.333 [{(1+0.00683)24 - 1}/0.00683]

                                 = 58124.91 - 16845.63

                                 = $41279.83

Susan should pay the bank $41279.83 on November 1, 2011.

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