Andrew Industries is contemplating issuing a $30-$year bond with a coupon rate of $7\mathrm{.}11\%($annual coupon payments$)$ and a face value of $$1,000.$ Andrew believes it can get a rating of A from Standard & Poor's. However, due to recent financial difficulties at the company, Standard & Poor's is warning that it may downgrade Andrew Industries' bonds to BBB$.$ Yields on A$-$rated, long$-$term bonds are currently $6\mathrm{.}56\%,$ and yields on BBB$-$rated bonds are $6\mathrm{.}73\%.$

a$.$ What is the price of the bond if Andrew Industries maintains the A rating for the bond issue?

b$.$ What will be the price of the bond if it is downgraded?