A corporate bond$$s credit rating provides a guide to its price. For company K$,$ the Aaa zerocoupon bonds yield $3\mathrm{.}5\%,$ and the Baa zero$-$coupon bonds pay $4\mathrm{.}5\%.$ Assume you are looking at a company K zero$-$coupon bond with a $$1,000$ face value and $7$ years to maturity. The specific bond you are looking at has an Aaa rating. Then, unexpectedly, some news causes that bond$$s rating to go from Aaa to Baa $($everything else constant$).$

a$.$ Calculate the bond$$s price under each rating. Use the specified yields as discount rates.

b$.$ Briefly explain why the yields vary according to the ratings.