Suppose someone takes out a home improvement loan for $3. the annual interest on the loan is 6% and is compounded monthly. the monthly payment is $600. let a 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 - this means in a given month interest is added first, and then the payment is applied to the resulting loan balance. (a) give a recursive definition for a,. including the recurrence relation and the base case. (you can readily check your thinking by setting up a spreadsheet to track the loan balance.) (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?