Pybus, Inc. is considering issuing bonds that will mature in $22$ years with an annual coupon rate of $11$ percent. Their par value will be $$$$1$ comma $000,$ and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds$$ and, if it$$ does, the yield to maturity on similar AA bonds is $8$ percent. $$ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A$$ rating, the yield to maturity on similar A bonds is $9$ percent. What will be the price of these bonds if they receive either an A or a AA$$ rating?

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Part $1$

a$.$ The price of the Pybus bonds if they receive a AA rating will be $$$

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enter your response here. $($Round to the nearest$$ cent.$)$