Consider a 30-year corporate bond paying 9 percent semi-annual coupon. The current yield to maturity is 11 percent.

a. Find the modified duration.

b. Refer to part a. If the interest increases by 10 basis points, what is the exact change in price?

c. Refer to part b. If the interest increases by 10 basis points, what is the approximate change in price?

d. What is the error of approximation?

e. Using 10 basis point interest rate changes, approximate the modified duration.