Suppose you borrow $12000 to buy a car. The loan is to be paid in 60 equal monthly installments at an interest rate of 5% per year. a. Assume that the payments are actually made continuously at whatever rate is needed to pay off the loan in 60 months. Determine the continuous rate per month that would be required. (Hint: the problem is easier if you think about it from the lenders point of view. The amount owed begins at $10,000. It increases continuously by a natural growth process and decreases continuously at a fixed rate. In 5 years, the amount owed is zero.) b. Compare the result of your differential equation model in part a. with the actual amount. You can find out how much the actual payment would be by consulting with a banker or other investment expert, or you can find appropriate charts in a book or on the internet. How good is the approximation?