A bond's credit rating provides a guide to its price. In December $2020,$ Aaa bonds yielded $4\mathrm{.}9\%,$ and Baa bonds yielded $5\mathrm{.}9\%.$ Some bad news causes a $10\%$ five$-$year bond to be unexpectedly downrated from Aaa to Baa. Assume face value is $$1,000.$

Note: Do not round intermediate calculations. Round your answers to $2$ decimal places.

a$.$ What is the bond's price if it is rated as Aaa?

b$.$ What is the bond's price if it is rated as Baa?