4. Two bonds are available for purchase in the financial markets. The first bond is a two-year, $1,000 bond that pays an annual coupon of 10 percent. The second bond is a two-year, $1,000 zero-coupon bond.

a. What is the duration of the coupon bond if the current yield to maturity (R) is 8 percent? 10 percent? 12 percent? (Hint: You may wish to create a spreadsheet program to assist in the calculations.)

b. How does the change in the yield to maturity affect the duration of this coupon bond?

c. Calculate the duration of the two-year zero-coupon bond with a yield to maturity of 8 percent, 10 percent, and 12 percent.

d. How does the change in the yield to maturity affect the duration of the zero coupon bond?

e. Why does the change in the yield to maturity affect the coupon bond differently than it affects the zero-coupon bond?