$($Related to Checkpoint $9\mathrm{.}3)($Bond valuation$)$ Pybus, Inc. is considering issuing bonds that will mature in $20$ years with an annual coupon rate of $11$ percent. Their par value will be $$1,000,$ and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds and, if it does, the yield to maturity on similar AA bonds is $12$ 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 $13$ percent. What will be the price of these bonds if they receive either an A or a AA rating?

a$.$ The price of the Pybus bonds if they receive a AA rating will be $$,($Round to the nearest cent.$)$

b$.$ The price of the Pybus bonds if they receive an A rating will be $$,($Round to the nearest cent.$)$