ABC bonds are currently priced at $959.45. The par value is $1,000, the coupon rate is 7% paid semi-annually and the bonds mature in five years. The Macauley duration is 4.29 years.

a. Calculate the yield to maturity

b. Calculate the modified duration based on the information above and your answer to (a)

c. Explain why modified duration is a better measure of a bonds sensitivity to changes in interest rates than maturity.

d. Determine the direction of the change in modified duration if:

(i) The bond matured in 10 years rather than 5 years

(ii) The coupon was 3% rather than 7%. (Note that you should not need to do any calculations for this part of the question. If you understand the concept of duration, you should be able to identify whether duration will increase or decrease without doing calculation.)

e. Define convexity. Explain how modified duration and convexity can be used to determine the approximate amount by which price will change for a given movement in interest rates.