4) (20 pt) Let 2% be the yield of the 1-year bond of face value $100 and semi-annual ( coupon $1. (a) Calculate the market price P of the bond. (b) Calculate the duration D and the modified duration DM. (c) Prove that the price-yield curve is convex. (d) When the yield changes slightly to 2.01%, estimate the percentage change in bond price in terms of the convexity C of the price-yield curve and the modified duration DM (e) Suppose the spot rates for 6-month and 1-yr zero-coupon bonds are 1% and 2%. What would be the fair price of the bond? Based on the market price calculated in (a) is the bond over-priced or under-priced