ii$.)$ Assume first that the interest rate for all horizons is $5\%.$ a$)$ What is the price of a $5-$year coupon bond that pays $$500$ for $4$ years and $$1,600$ in the fifth year? What is its duration? What is the modified duration of this bond? b$)$ Assume first that the interest rate for all horizons is $5\%.$ c$)$ Let us assume that the interest rate changes by $50$ basis point from $5\%$ to $5\mathrm{.}5\%,$ what is the convexity and how the presence of convexity affects the resulting change in its price? d$)$ Let us assume that the interest rate changes by $100$ basis points from $5\%$ to $6\%,$ how the presence of convexity affects the resulting change in its price? Compare it with part iii and explain the results. e$)$ As CFO of a leading bank, how do interest rate change affect your balance sheet? Hint: think of your balance sheet and debt interest payments on varying maturities of debt.