zero-coupon bond

1. Assume that the term structure is flat. Consider two pure discount bonds 1 and 2. Bond 1 matures in T years and bond 2 matures in 2T years. Is bond 2 “twice as sensitive to a 1% upward shift of the term structure” as bond 1?
2. Consider a zero-coupon bond with nominal $100 and annual yield of 5%, with one year to maturity. You believe that after one week the yield will change from 5% to 5.5%. Find the expected change in the bond price in three ways:
a. Exactly, computing the new price
b. Approximately, using the initial duration
c. Approximately, using the initial duration and convexity