A 20-year, 6.500% annual payment bond settles on a coupon date. The bond's yield to maturity is 9.400%.

(a) What is the bonds Macauley Duration (show your work, like you did in problem (16) above.)

(b) What is the bonds approximate modified duration? Use yield changes of +/- 30 bps around the yield to maturity for your calculations.

(c) Calculate the approximate convexity for the bond.

(d) Calculate the change in the full bond price for a 40 bps change in yield.