$[$Chapter $6\mathrm{.}13]$ You observe the yields of the following Treasury securities $($all yields are shown on a bond$-$equivalent basis$)$: Year $($Period$)$Yield to Maturity $(\%)$Spot Rate $(\%)$Year $($Period$)$Yield to Maturity $(\%)$Spot Rate $(\%)0\mathrm{.}5(1)1\mathrm{.}0(2)1\mathrm{.}5(3)2\mathrm{.}0(4)2\mathrm{.}5(5)3\mathrm{.}0(6)3\mathrm{.}5(7)4\mathrm{.}0(8)4\mathrm{.}5(9)5\mathrm{.}0(10)5\mathrm{.}255\mathrm{.}255\mathrm{.}505\mathrm{.}505\mathrm{.}755\mathrm{.}766\mathrm{.}00?6\mathrm{.}256\mathrm{.}286\mathrm{.}50?6\mathrm{.}756\mathrm{.}827\mathrm{.}007\mathrm{.}107\mathrm{.}257\mathrm{.}387\mathrm{.}507\mathrm{.}675\mathrm{.}5(11)6\mathrm{.}0(12)6\mathrm{.}5(13)7\mathrm{.}0(14)7\mathrm{.}5(15)8\mathrm{.}0(16)8\mathrm{.}5(17)9\mathrm{.}0(18)9\mathrm{.}5(19)10\mathrm{.}00(20)7\mathrm{.}757\mathrm{.}978\mathrm{.}008\mathrm{.}278\mathrm{.}258\mathrm{.}598\mathrm{.}508\mathrm{.}928\mathrm{.}759\mathrm{.}259\mathrm{.}009\mathrm{.}619\mathrm{.}259\mathrm{.}979\mathrm{.}5010\mathrm{.}369\mathrm{.}7510\mathrm{.}7710\mathrm{.}0011\mathrm{.}20$ 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 forward rate starting in the sixth year $(12$f$13)?$