Problem 8. Given the following price information for four annual coupon bonds, and assuming that all four bonds are trading to yield 5%. 1. Calculate the price (present value) of each bond You can use the following formula PV=rPMT[1(1+r)N1]+(1+r)NFV PV: present value (bond's price); PMT: annual coupon payment; r: yield to maturity; N: maturity. 2. Assuming a 25 basis, and 50 basis point rate change (y=0.0025, and y=0.0050) a. Calculate Macaulay duration using the closed-form formula MacDur ={r1+rc[(1+r)N1]+r1+r+[N(cr)]}(t/T) c : coupon rate; t/T : fraction of the period that has gone; T : time-period between two coupon payments (here 365 days); N: maturity b. Calculate modified duration c. Calculate the approximate duration d. Calculate the convexity adjustment