Andrew Industries is contemplating issuing a$30-$year bond with a coupon rate of $7\mathrm{.}47\%($annual coupon$$ payments$)$ and a face value of $ $1$ comma $000.$ Andrew believes it can get a rating of A from Standard and$$ Poor's. However, due to recent financial difficulties at the$$ company, Standard and$$ Poor's is warning that it may downgrade Andrew Industries bonds to BBB$.$ Yields on$$ A$-$rated, long$-$term bonds are currently $6\mathrm{.}97\%,$ and yields on$$ BBB$-$rated bonds are $7\mathrm{.}37\%.$

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

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