Chapter 5.4, Problem 25E

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.

Kevin and Roxanne Gahagan did not have sufficient cash to pay their income taxes. However, they had previously set up a line of credit with their bank. On April 15, they wrote a check to the Internal Revenue Service on their line of credit for $6, 243. The line's interest rate is 5.75%.

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

b. The Gahagans decided that it would be in their best interests to get this loan paid off in eight months. Find the size of the monthly principal-plus-interest payment that would accomplish this. HINT In effect, the Gahagans are converting the loan to an amortized loan.

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

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