Q$3)$ A company has a $$1,000$ face value that matures $4$ years from today and has a yield of $6\%($APR with semiannual compounding$).$ The bond pays semiannual coupons at an annual rate of $9\%.$

a$)$ What is the Macaulay Duration of the bond?

b$)$ Calculate the bonds modified duration?

c$)$ What is the approximate percentage change in the price of the bond if the yield changes to $7\mathrm{.}5\%$