$\backslash$table$[[$Year $($Period$),$Yield to Maturity $(\%)$ Spot Rate $(\%),$Year $($Period$),$Yield to Maturity $(\%)$Spot Rate $(\%),,],[0\mathrm{.}5(1),5\mathrm{.}25,5\mathrm{.}25,5\mathrm{.}5(11),7\mathrm{.}75,7\mathrm{.}97],[1\mathrm{.}0(2),5\mathrm{.}50,5\mathrm{.}50,6\mathrm{.}0(12),8\mathrm{.}00,8\mathrm{.}27],[1\mathrm{.}5(3),5\mathrm{.}75,5\mathrm{.}76,6\mathrm{.}5(13),8\mathrm{.}25,8\mathrm{.}59],[2\mathrm{.}0(4),6\mathrm{.}00,?,7\mathrm{.}0(14),8\mathrm{.}50,8\mathrm{.}92],[2\mathrm{.}5(5),6\mathrm{.}25,?,7\mathrm{.}5(15),8\mathrm{.}75,9\mathrm{.}25],[3\mathrm{.}0(6),6\mathrm{.}50,?,8\mathrm{.}0(16),9\mathrm{.}00,9\mathrm{.}61],[3\mathrm{.}5(7),6\mathrm{.}75,?,8\mathrm{.}5(17),9\mathrm{.}25,9\mathrm{.}97],[4\mathrm{.}0(8),7\mathrm{.}00,?,9\mathrm{.}0(18),9\mathrm{.}50,10\mathrm{.}36],[4\mathrm{.}5(9),7\mathrm{.}25,?,9\mathrm{.}5(19),9\mathrm{.}75,10\mathrm{.}77],[5\mathrm{.}0(10),7\mathrm{.}50,?,10\mathrm{.}00(20),10\mathrm{.}00,11\mathrm{.}20]]$

All the securities maturing from $1\mathrm{.}5$ years on are selling at par. The $0\mathrm{.}5$ and $1\mathrm{.}0-$year securities are zero$-$coupon instruments. Answer the below questions.

$($a$)$ Calculate the missing spot rates.

$($b$)$ What should the price of a $6\%$ six$-$year Treasury security be$?$

$($c$)$ What is the six$-$month forw ward rate starting in the sixth year?$|$