Show me the steps to solve analyst at Aurora Fixed Income Management. Your team is evaluating a new corporate bond issue as a potential investment. The bond is a $7-$year semiannual bond, with a $\backslash (5\backslash \%\backslash )$ annual coupon rate, a face value of $\backslash (\backslash$$ $1,000\backslash ),$ and a market yield of $\backslash (4\backslash \%\backslash )$ annually. The bond is currently trading in the secondary market. The team wants to assess the value and interest rate sensitivity of this bond. $[1]$ Calculate the coupon payment for each period. $(3$ mark$)[2]$ Calculate the bond price. $(3$ marks$)[3]$ Calculate the Macaulay duration and compute the modified duration. $(8$ marks$)[4]$ Estimate the change in bond price if interest rates rise by $50$ basis points, what is the new bond price? $(6$ marks$)$ Q$2.$ A semiannual bond issued by Titan Capital pays a $6\backslash \%$ annual coupon, has a maturity of $10$ years, and is callable after $3$ years at $\backslash (\backslash$$ $1,030\backslash ).$ The bond has a face value of $\backslash (\backslash$$ $1,000\backslash )$ and currently trades at $\backslash$$$1,070$ in the secondary market. $[1]$ Calculate the annual coupon income and current yield based on the market price. $(6$ marks$)[2]$ Discuss whether the Yield to Call $($YTC$)$ is likely higher or lower than the current yield, and explain why. $(6$ marks$)[3]$ Explain why conservative investors prefer to evaluate callable bonds using the Yield to Worst $($YTW$)$ instead of the Yield to Maturity $($YTM$).(6$ marks$)$ Q$3.$ You are a fixed income analyst at Zenith Asset Management. You are tasked with evaluating the interest rate sensitivity of a long$-$term, option$-$free semiannual bond as part of a durationhedging strategy. The bond has a face value of $\backslash (\backslash$$ $1,000\backslash )$ and pays a $\backslash (4\backslash \%\backslash )$ annual coupon, for a total maturity of $20$ years, and the market yield is $\backslash (6\backslash \%\backslash )$ per annum. You may assume that all cash flows are certain and there is no default risk. The fund expects a $75$ basis point decline in interest rates and wants to assess how much the bond's price might change in response. $[1]$ Calculate the modified duration of the bond. $(7$ marks$)[2]$ Calculate the convexity of the bond. $(7$ marks$)$