A Treasury bond has a maturity of 2 years and pays a 9% coupon rate with semiannual payments. The bond is traded at par, and the face value of the bond is $1,000.

1. What are the duration and convexity of the bond? What is the yield to maturity on the bond?
2. To match the duration of a lump sum loan maturing in 3 years, what is the required proportion of the Treasury bond to mix with a zero-coupon bond maturing in 5 years.
3. If the yield to maturity of the Treasury bond suddenly changed to 7.6%, what price of the Treasury bond would be predicted by the duration-with-convexity rule? What is the percentage error of that rule?