3) A bond has four years to maturity, a 10% annual coupon and a par value of $100. The bond pays a continuously compounded interest of 8%.

a. What would the actual percentage change in the price of the bond be if the interest rate goes up from 8% to 9%?

b. What would be the percentage change in the price of the bond implied by the duration approximation?

c. What would be the percentage change in the price of the bond implied by the duration plus convexity approximation?

d. Why does adding the convexity term to the approximation improve it?