You observe the yields of the following Treasury securities at below $($all yields are shown$$on a bond$-$equivalent basis$).$ All the securities maturing from $1\mathrm{.}5$ years onwards are$$selling at par. The $0\mathrm{.}5$ and $1\mathrm{.}0-$year securities are zero$-$coupon instruments.$2$Year$($Period$)$Yield to Maturity$(\%)$Spot Rate$(\%)$Year$($Period$)$Yield to Maturity$(\%)$Spot$$Rate $\%0\mathrm{.}5(1)5\mathrm{.}255\mathrm{.}255\mathrm{.}5(11)7\mathrm{.}757\mathrm{.}971\mathrm{.}0(2)5\mathrm{.}505\mathrm{.}506\mathrm{.}0(12)8\mathrm{.}008\mathrm{.}271\mathrm{.}5(3)5\mathrm{.}755\mathrm{.}766\mathrm{.}5(13)8\mathrm{.}258\mathrm{.}592\mathrm{.}0(4)6\mathrm{.}00?7\mathrm{.}0(14)8\mathrm{.}508\mathrm{.}922\mathrm{.}5(5)6\mathrm{.}25?7\mathrm{.}5(15)8\mathrm{.}759\mathrm{.}253\mathrm{.}0(6)6\mathrm{.}50?8\mathrm{.}0(16)9\mathrm{.}009\mathrm{.}613\mathrm{.}5(7)6\mathrm{.}75?8\mathrm{.}5(17)9\mathrm{.}259\mathrm{.}974\mathrm{.}0(8)7\mathrm{.}00?9\mathrm{.}0(18)9\mathrm{.}5010\mathrm{.}364\mathrm{.}5(9)7\mathrm{.}25?9\mathrm{.}5(19)9\mathrm{.}7510\mathrm{.}775\mathrm{.}0(10)7\mathrm{.}50?10\mathrm{.}00(20)10\mathrm{.}0011\mathrm{.}20($a$)$ Calculate the missing spot rates.$($b$)$ What should the price of a $6\%5\mathrm{.}5-$year Treasury security be$?($c$)$ What is the six$-$month forward rate starting in the seventh year?