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 expressed as an 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 sum of the rate durations is approximately equal to the duration. They may not be exactly the same because the yield curve is not flat, but if you have computed (a) through (d) correctly then they should be reasonably similar.