A $$1,000-$par bond with a $6\%$ coupon paid semi$-$annually has $9$ years left to maturity. The bond

is currently trading at a yield to maturity of $5\mathrm{.}75\%.$

A$.$ What is the Macaulay duration of the bond? Hint: Use spreadsheet.

B$.$ What is the modified duration of the bond?

C$.$ What is the convexity of the bond?

D$.$ If interest rates fall by $60$ bps$,$ what is the predicted $\%$ price change in the bond based on

duration?

E$.$ If interest rates fall by $60$ bps$,$ what is the predicted $\%$ price change in the bond based on

convexity?

F$.$ If interest rates fall by $60$ bps$,$ what is the predicted $\%$ price change in the bond based on

duration and convexity?