Fabozzi, ${10}^{th}$ edition, Chapter $6,$ Problem #$13(40$ points$)$ You observe the yields of the following

Treasury securities $($all yields are shown on a bond$-$equivalent basis$)$:

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?