Andrew Industries is contemplating issuing a $30-$year bond with a coupon rate of $7\mathrm{.}06\%($annual coupon$$ payments$)$ and a face value of $$$$1000.$ Andrew Industries believes it can get a rating of A from Standard$$ & Poor's.$$ However, due to recent financial difficulties at the$$ company, Standard$$ & Poor's is warning that it may downgrade Andrew Industries$\text{'}$ bonds to BBB$.$ Yields on$$ A$-$rated, long$-$term bonds are currently $6\mathrm{.}41\%,$ and yields on$$ BBB$-$rated bonds are $6\mathrm{.}82\%.$

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$$ downgraded? the bond if it is$$ downgraded?