Pybus, Inc. is considering issuing bonds that will mature in $19$ years with an annual coupon rate of $9$ 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 AA rating?

AA rating:

A rating: