Suppose the Treasury zero curve is 0.5% for 6 months and 0.75% for 1 year, as APRs with semi-annual compounding. Consider a 2% Treasury bond with 1 year remaining.

(a) Determine the price of the bond.

(b) Determine the yield-to-maturity (express as APR with semi-annual compounding).

(c) Determine the duration (either modified or effective) based on the yield-to-maturity.

(d) Determine the 0.5-year and 1.0-year rate durations empirically.

(e) Verify that the dollar-weighted sum of the rate durations is approximately equal to the duration. If you have computed (a) through (d) correctly then these should be similar. (They may not be exactly the same because the yield curve is not flat.)