Consider a three$-$year option$-$free bond paying an $11\%$ percent annual coupon and selling at par value.

Required:

a$)$ Calculate the duration of the bond.

b$)$ If the yield to maturity is expected to change by $175$ b$.$p$.$ in either direction:

i$.$ Using the duration rule, determine the price of the bond at the new yields.

ii$.$ Assuming the convexity of the bond is $15,$ use the duration$-$with$-$convexity rule to determine the price for the bond at the new yield.

iii. Compare the results obtained in part i and ii$.$ What observations do you make?

Show all workings. Round$-$off all final answers to two decimal places. You do not need to include or show the formulas used in your answer.