(Problem 4.37) On September 1, 1998, Susan Chao bought a motorcycle for $10,000. She paid $1,000 down and financed the balance with a five-year loan at a stated annual interest rate of 9.6 percent, compounded monthly. She started the monthly payment exactly one month after the purchase, i.e., October, 1998. In the middle of October, 2000, she got a new job and decided to pay off the loan. If the bank charges her 1 percent prepayment penalty based on the loan balance, how much should she pay the bank on November 1, 2000?
This is a problem from Steven Ross's wonderful book(Corporate finance). I'm not sure about my interpretation and solution, so I hope someone can check it for me
My solution: Since she paid $1000 right away, she owes 10000-1000=$9000 on Sep 1,1998. Now, the future value of this loan on October 1,2000= FV(0.096/12,25,0,-9000)= $10983.88 (n=25 because it's from September 1,1998 to October 1, 2000). In addition, monthly payment= PMT(0.096/12,60,-9000)= $189.46. Thus, the future value of Chao's payment on October 1, 2000= FV(0.096/12,24,-189.46)=$4990.89.
The remaining loan (on October 1,2000) =10983.88 - 4990.89=$5992.99. Now, since the bank charges her 1 percent prepayment penalty when she pays off the remaining loan on mid. October 2000, she will owes 5992.99*0.01=$59.9299. Thus, on November 1,2000, she needs to pay 59.9299*(1+0.096/24)= $60.16972
This is a problem from Steven Ross's wonderful book(Corporate finance). I'm not sure about my interpretation and solution, so I hope someone can check it for me
My solution: Since she paid $1000 right away, she owes 10000-1000=$9000 on Sep 1,1998. Now, the future value of this loan on October 1,2000= FV(0.096/12,25,0,-9000)= $10983.88 (n=25 because it's from September 1,1998 to October 1, 2000). In addition, monthly payment= PMT(0.096/12,60,-9000)= $189.46. Thus, the future value of Chao's payment on October 1, 2000= FV(0.096/12,24,-189.46)=$4990.89.
The remaining loan (on October 1,2000) =10983.88 - 4990.89=$5992.99. Now, since the bank charges her 1 percent prepayment penalty when she pays off the remaining loan on mid. October 2000, she will owes 5992.99*0.01=$59.9299. Thus, on November 1,2000, she needs to pay 59.9299*(1+0.096/24)= $60.16972