Assume that the yield curve is flat at 5.1%. The bond has 3 years to maturity, and pays coupons annually. The face value of the bond is $100, and the bond pays a 5.38% coupon rate.

a) Compute the convexity of the bond?

b) Suppose there is a parallel shift in all interest rates by +2.35%. Compute the value of the bond price following the change in interest rates by applying the duration-based first-order approximation.

c)Suppose there is a parallel interest rate shift in all interest rates by +2.35%. Compute the value of the bond price following the change in interest rates by applying the second-order approximation with both duration and convexity terms.

d)Suppose there is a parallel shift in all interest rates by +2.35%. Compute the exact value of the bond price following the change in interest rates.