Please show your calculations for the following question:

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 is 8 percent? 10 percent? 12 percent?

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

c. Calculate the duration of the 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?