Problem 1. Suppose we want to know how much we can borrow for a car if we can pay back $100 each month and if the bank charges 12% annual interest compounded monthly. We need to pay the loan off by the end of 5 years. (Note: we pay $100 each month right after the bank assesses the interest on the loan balance.) Let yn denote the amount we owe at the end of the n-th month. a.) What does yo represent in the problem? b.) What is the monthly interest? c.) Find Yn+1 in terms of yn, and simplify so it is in the form Yn+1 = 2 . Yn + b. d.) What are we solving for here? In other words, what does "paying off the loan by the end of 5 years mean? Write an equation (this is similar to what we did in Example 4 when we solved for how much money was in the bank at the end of 10 years). e.) Solve the equation you wrote in part d