19. 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.

20. Consider the bond from problem (19) above.

(a) Calculate the approximate convexity for the bond.

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

All prices and interest rates must be expressed to THREE decimal places. You must show your work for every problem