A$)$ The portfolio manager of smith company has excess cash that is to be invested for four years. The manager can purchase four$-$year treasury notes that offer a $9$ percent yield. Alternatively, she can purchase new $20-$year treasury bonds for $ $2\mathrm{.}9$ million that offer a par value of $ $3$ million and an $11$ percent coupon rate with annual payments. The manager expects that the required return on these same $20-$year bonds will be $12$ percent four years from now.

i$)$ What is the forecasted market value of the twenty$-$ year bonds in four years?

ii$)$ Which investment is expected to provide a higher yield over the four$-$ year period?

B$-$ a two$-$year bond has duration equal to $1\mathrm{.}92$ years and a $10$ percent yield to maturity.

i$)$ How much is its modified duration?

ii$)$ Assume that bond yields rise by $0\mathrm{.}30\%.$ What is the estimated percentage drop in the bonds price?