Suppose someone takes out a home improvement loan for $30000. 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?
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Home » Mathematics » Suppose someone takes out a home improvement loan for $30000. 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.