home mort- 40. Paying Down a Mortgage You took a $200,000 gage at an annual interest rate of 3%. Suppose that the loan is amortized over a period of 30 years, and let P(t) denote the amount of money (in thousands of dollars) that you owe on the loan after t years. A reasonable estimate of the rate of change of P is given by P(t)-4.1107e0.03t. (a) Approximate the net change in P after 20 years. (b) What is the amount of money owed on the loan after 20 years? (c) Verify that the loan is paid off in 30 years by com- puting the net change in P after 30 years. 41. Mortgage Using the data from the previous exercise, find P(t). [Hint: P(0) 200.]