Market Curve and Calculating Spot Rates

You observe the yields of the following Treasury securities

Year

$($Period$)$

Yield to Maturity

$(\%)$

Spot Rate

$(\%)$

Year

$($Period$)$

Yield to Maturity

$(\%)$

Spot Rate

$(\%)$

$0\mathrm{.}5(1)5\mathrm{.}255\mathrm{.}255\mathrm{.}5(11)7\mathrm{.}757\mathrm{.}97$

$1\mathrm{.}0(2)5\mathrm{.}505\mathrm{.}506\mathrm{.}0(12)8\mathrm{.}008\mathrm{.}27$

$1\mathrm{.}5(3)5\mathrm{.}755\mathrm{.}766\mathrm{.}5(13)8\mathrm{.}258\mathrm{.}59$

$2\mathrm{.}0(4)6\mathrm{.}00?7\mathrm{.}0(14)8\mathrm{.}508\mathrm{.}92$

$2\mathrm{.}5(5)6\mathrm{.}25?7\mathrm{.}5(15)8\mathrm{.}759\mathrm{.}25$

$3\mathrm{.}0(6)6\mathrm{.}50?8\mathrm{.}0(16)9\mathrm{.}009\mathrm{.}61$

$3\mathrm{.}5(7)6\mathrm{.}75?8\mathrm{.}5(17)9\mathrm{.}259\mathrm{.}97$

$4\mathrm{.}0(8)7\mathrm{.}00?9\mathrm{.}0(18)9\mathrm{.}5010\mathrm{.}36$

$4\mathrm{.}5(9)7\mathrm{.}25?9\mathrm{.}5(19)9\mathrm{.}7510\mathrm{.}77$

$5\mathrm{.}0(10)7\mathrm{.}50?10\mathrm{.}00(20)10\mathrm{.}0011\mathrm{.}20$

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$?$