A two-year amortizing bond has a coupon rate of 4% and pays its coupons semi annually. Coupon payments are based upon the outstanding face value at the start of the coupon period. It has a face value of 200 and 50 of the face value is amortized every half year. The yield to maturity is 1% per year.

a) Calculate the price of the bond.

b) Calculate the duration of the bond.

c) Calculate the convexity of the bond.

d) If the yield to maturity rises to 4% estimate the price of the bond using both duration and convexity. (Do not calculate the actual new price of the bond)

e) Explain why the duration and convexity are used jointly to provide the estimate of the price change of the bond than just using duration.