Andrew Industries is contemplating issuing a $30-$year bond with a coupon rate of $4\mathrm{.}41\%($annual coupon payments$)$ and a face value of $$1,000.$ 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 $3\mathrm{.}91\%,$ and yields on BBB$-$rated bonds are $4\mathrm{.}31\%.$

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?

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

The price of the bond maintaining the A rating is $$33\mathrm{.}33.($Round to the nearest cent.$)$