Suppose someone takes out a home improvement loan for $30,000. The annual interest on the loan is 6% compounded monthly. The monthly payment is $600. Let an denote the amount owed at the end of the nth month. The payments start the first month and are due the last day of every month. a. Give a recurrence relation for an. Don't forget the basis (also called the initial conditions). Suppose the borrower would like a lower monthly payment. How large does the monthly payment need to be to ensure that the amount owed decreases every month? b