Question 5 A mortgage has maturity T equal to 20 years. The principal is Po = $100,000. The interest rate of this mortgage, i.e., yield to maturity, is y = 10%. The fixed mortgage payments are paid annually. (a) What is the fixed mortgage payment of each year M? (2 marks) (b) The mortgage payment of year t, M, can be decomposed into two parts: the interest payment It and the principal repayment Rt. The interest payment I, is equal to the remaining principal at the beginning of year t multiplied by the interest rate of the contract y. Then, the principal repayment of year t is Rc = M-It. The remaining principal at the beginning of year t+1 is equal to the remaining principal at the beginning of year t minus Rt. Calculate 11, R1, 12, and R2. (4 marks) (c) Derive the general formulas for It and Rt. 1stsT with only t, T, y, and Po in the expressions. Also verify that the sum of the repayments of these T years is equal to Po. (8 marks) Hint: one way to solve it is to use mathematical induction. Try to write down the formulas of 14 and Rt for the first few years and see the pattern of the formulas