Consider a bond that pays an annual coupon of 8%, a par value of $1,000, and 4 years to maturity. the current annual yield on the bond is 7%.

a) calculate the bond's Macaulay and modified duration. calculate the bond's convexity.

b) if the yield changes to 5% (instantaneously), what is the new bond price? what is the percentage change in the bond's price?

c) what is the approximate percentage change in price using the modified duration formula? what is the approximate percentage change in price using the convexity and duration adjustment formula?

d) describe the observed differences in your answers to parts b and c.