Assume that a bond has $5$ years left to maturity and pays its $6\%$ coupon semi$-$annually and

the prevailing interest rate for this bond is $8\%.$ The face value of the bond is $$1,000.$

a$.$ Calculate the price of the bond.

$(6$ Marks$)$

b$.$ Compute the duration and modified duration of the bond.

$(10$ Marks$)$

c$.$ Using modified duration, compute the percentage change in price of the bond if the

interest rate increases by $50$ basis points.

$(3$ Marks$)$

d$.$ Define convexity and explain how modified duration and convexity are used to

approximate the bond's percentage change in price, given a large change in interest rates.

$(6$ Marks$)$