You observe the following Treasury yields $($all yields are shown on a bond equivalent basis$)$:

Year $($Period$)$ Yield to Maturity $(\%)$ Spot Rate $(\%)$

$0\mathrm{.}5(1)10\mathrm{.}0010\mathrm{.}00$

$1\mathrm{.}0(2)9\mathrm{.}759\mathrm{.}75$

$1\mathrm{.}5(3)9\mathrm{.}509\mathrm{.}48$

$2\mathrm{.}0(4)9\mathrm{.}259\mathrm{.}22$

$2\mathrm{.}5(5)9\mathrm{.}008\mathrm{.}95$

$3\mathrm{.}0(6)8\mathrm{.}75?$

$3\mathrm{.}5(7)8\mathrm{.}50?$

$4\mathrm{.}0(8)8\mathrm{.}258\mathrm{.}14$

$4\mathrm{.}5(9)8\mathrm{.}007\mathrm{.}86$

$5\mathrm{.}0(10)7\mathrm{.}757\mathrm{.}58$

$5\mathrm{.}5(11)7\mathrm{.}507\mathrm{.}30$

$6\mathrm{.}0(12)7\mathrm{.}257\mathrm{.}02$

$6\mathrm{.}5(13)7\mathrm{.}006\mathrm{.}74$

$7\mathrm{.}0(14)6\mathrm{.}756\mathrm{.}46$

$7\mathrm{.}5(15)6\mathrm{.}506\mathrm{.}18$

$8\mathrm{.}0(16)6\mathrm{.}255\mathrm{.}90$

$8\mathrm{.}5(17)6\mathrm{.}005\mathrm{.}62$

$9\mathrm{.}0(18)5\mathrm{.}755\mathrm{.}35$

$9\mathrm{.}5(19)5\mathrm{.}505\mathrm{.}07$

$10\mathrm{.}0(20)5\mathrm{.}254\mathrm{.}80$

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 following questions.

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

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