$($Related to Checkpoint$9\mathrm{.}3)($Bond valuation$)$ is considering issuing bonds that will mature in $23$ years with an annual coupon rate of $11$ percent. Their par value will be $$$$1000,$ and the interest will be paid semiannually. is hoping to get a AA rating on its bonds$$ and, if it$$ does, the yield to maturity on similar AA bonds is $10\mathrm{.}5$ percent. $$ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A$$ rating, the yield to maturity on similar A bonds is $11\mathrm{.}5$ percent. What will be the price of these bonds if they receive either an A or a AA$$ rating?