2. Let P0 be the price at time 0 of an N-period bond with a yield per period r, a coupon C and a par value PN. Denote by D0 the duration of the bond. Let H be an integer such that 0HN. Denote by RH the value at time H of the first H coupons reinvested at the rate r, and let PH be the selling price of the bond at time H assuming no change in interest rates, that is, PH is the price of an (NH)-period bond with the same yield per period r, the same coupon C and the same par value PN. (a) Find the reduced form expression of P0,RH and PH. (b) Prove that rRH>0andrPHH,D00andrPHH,D0