Chapter 5.4, Problem 27E

For Exercises 25-28, note the following information. A line of credit is an agreement between a bank and a borrower by which the borrower can borrow any amount of money (up to a mutually agreed-upon maximum) at any time, simply by writing a check. Typically, monthly simple interest payments are required, and the borrower is free to make principal payments as frequently or infrequently as he or she wants. Usually, a line of credit is secured by the title to the borrower’s house, and the interest paid to the bank by the borrower is deductible from the borrower's income taxes.

Homer Simpson had his bathroom remodeled. He did not have sufficient cash to pay for it. However, he had previously set up a line of credit with his bank. On July 12, he wrote a check to his contractor on his line of credit for $\$12,982$ . The line's interest rate is $8.25\%$.

a. Find the size of the required monthly interest payment.

b. Homer decided that it would be in his best interests to get this loan paid off in seven months. Find the size of the monthly principal-plus-interest payment that would accomplish this.

HINT: In effect, Simpson is converting the loan to an amortized loan.

c. Prepare an amortization schedule for all seven months of the loan.

d. Find the amount of line of credit interest that Simpson could deduct from his taxes next year.