A$$ BBB$-$rated corporate bond has a yield to maturity of $9\mathrm{.}2\%9\mathrm{.}2\%.$ A U$.$S$.$ Treasury security has a yield to maturity of $7\mathrm{.}7\%7\mathrm{.}7\%.$ These yields are quoted as APRs with semiannual compounding. Both bonds pay$$ semi$-$annual coupons at a rate of $8\mathrm{.}5\%8\mathrm{.}5\%$ and have $55$ years to maturity.$$

a$.$ What is the price$($expressed as a percentage of the face$$ value$)$ of the Treasury$$ bond?

b$.$ What is the price$($expressed as a percentage of the face$$ value$)$ of the$$ BBB$-$rated corporate$$ bond?

c$.$ What is the credit spread on the BBB$$ bonds?