The $5-$Year U$.$S$.$ Treasury Bill yields $10\%$ and the $10-$

Year yields $15\%.$ Terra Co$.$ has a bond outstanding with a

$11\%$ coupon, rated AA maturing in $10$ years. AA rated

corporate bonds yield $30$ basis points $($bps$,$ remember $1$ bp $-$

$\frac{1}{100}$ of $1\%)$ more than treasuries across the run $($i$.$e$.$ whether

$2$ years, $5$ years, ete$).$

a$.$ What is YTM of Terra Co$.?$

b$.$ Does the bond trade at premium, par, discount?

c$.$ If the economy goes into recession, what will spread do $?$