Exercise 6 (Each part 1 marks). (a) Consider an annuity that pays 1 every quarter for M years. In other words, the payment times are T tt,t + . Show that the value at present time t is T" 4 assuming the quarterly compounded interest rate has constant value r4. (b) A fixed rate bond with notional N, coupon c, start date To, maturity T,, and term length a is an asset that pays N at time T, and coupon payments aNeat times T for i,.,n, where Ti+1-Ti +a. It is equivalent to an annuity plus N ZCBs. Consider a fixed rate bond with notional N and coupon c that starts now, matures M years from now, and has quarterly coupon payments. Show that the value at present time t is assuming the quarterly compounded interest rate has constant value r