Exercise 8.2.2: Refinancing a loan. About Suppose someone takes out a home improvement loan for $30,000. The annual interest on the loan is 6% and is compounded monthly. The monthly payment is $600. Let an denote the amount owed at the end of the nth month. The payments start in the first month and are due the last day of every month. (a) Give a recurrence relation for an. Don't forget the base case. (b) Suppose that 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