$2.$ Fixed$-$Income Application $-$ Bond Cash Flows and Risks: Suppose you purchase a corporate bond with the following features: a face $($par$)$ value of $\backslash (\backslash$$ $1,000\backslash ),$ an annual coupon rate of $\backslash (5\backslash \%\backslash ),$ and a maturity of $10$ years. The bond pays interest annually $($once per year$).$ Answer the following: $-($a$)$ How much annual interest $($coupon payment$)$ in dollars will you receive each year from this bond? Show how you calculate this amount. $-($b$)$ What amount will you receive from the bond at maturity $($at the end of $10$ years$),$ in addition to the final interest payment? $-($c$)$ Explain qualitatively how a rise in market interest rates shortly after your purchase would likely affect the market price of this bond. For instance, if new bonds are being issued at higher yields than $\backslash (5\backslash \%\backslash ),$ what happens to the value of your $\backslash (5\backslash \%\backslash )$ bond on the secondary market? Why does this price change occur? $($Describe the inverse relationship between interest rates and bond prices in your explanation.$)-($d$)$ Now consider that the issuing company's credit rating is downgraded during the life of the bond $($meaning the market perceives a higher risk of default$).$ What impact would this have on the yield investors demand for the bond and consequently on the bond's market price? Explain the intuition $($i$.$e$.$ higher default risk leads to higher required yield, thus lower price for existing bonds$).$