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 $5\%$ four$-$year Treasury security be$?$