$1,$ A $6\%$ semiannual coupon bond has paid the first coupon, it happened $91$ days ago. It has nine coupon payments left as it payssemiannually. $($There are $182$ days in a coupon period.$)$ The bond currently sells at a net $95\%$ of par. $($total: $8$ points$)$

a$,$ What is the Macaulay duration of the bond? $(3$ points$)$

b$,$ How long should the bond be held from now on to have an offsetting coupon reinvestment risk and market price risk? What risk willdominate if the investor decides to sell the bond three years later? $(2$ points$)$

c$,$ How will the bond's price change if the YTM changes by $50$ basis points upwards? $(1$ point$)$

d$,$ How would you estimate the new price of the bond after the $50$bp change by using the modified duration formula? What is thepercentage error of your estimation? $(2$ points$)$