Question 2. Annuities and bonds. a) Suppose that the current time t is at the beginning of the year. Consider an annuity that pays 1 at the end of every quarter for M years. Express the value at present time t as a sum, and then find a formula for the sum. Assume the quarterly compounded interest rate has constant value r4. b) A fixed rate bond with notional N, coupon c, start date To, maturity Tn, and term length a is an asset that pays N at time Tn and coupon payments aNc at times T; for i = 1,...,n, where T; = To +ia. Consider a fixed rate bond with notional N and coupon c that starts now, matures M years from now, and has quarterly coupon payments. Assume that the quarterly compounded interest rate has constant value r4. Consider how the bond could be replicated by annuities and zero coupon bonds. Then find the value of the bond at the current time. Your answer should be formula involving N, M,c, r4