$1)$ Credit Rating Yield

AAA $3\%$

AA $3\mathrm{.}2\%$

A $3\mathrm{.}5\%$

BBB $3\mathrm{.}8\%$

BB $4\mathrm{.}5\%$

B $5\mathrm{.}25\%$

a$)$ Given the yields for bonds with different credit ratings, what would be the fair price of a $5-$year maturity bond, which currently has identical risk to a bond rated $$A$,$ if it has a coupon rate of $12\%$ paid annually, and a par value of $$1,000?$

b$)$ What would be the price of the bond $3$ years from today if the bond is expected to be downgraded to $$BBB$$ at the end of the $3$rd year?