A 10- year U.S Treasury bond with face value of $1,000 pays a coupon of 5.5% (2.75% of face value every six months). The reported yield to maturity in the market for this bond today is 6.0% (a semiannually discount rate of 6.0/2=3.0%)

1. What is the present value of the bond today (at t=0)?

2. Generate a graph or table showing how the bonds present value at t =0 changes for semi-annually compounded interest rate changes of 50, 100 and 200 basis points (i.e. for the following values for the semi-annually interest rate: 2.50%, 3.50%, 2%, 4%, 1% and 5%). Are those changes in price symmetrical?

3. Now use the same US Treasury bond indicated in the initial statement and compare it with two Treasury notes with the same coupon rate than the previous Treasury bond. They have also a face value of $1,000 and pay an annual coupon rate of 5.5%, payable each semester (i.e. 2.75% each semester). The only difference amongst all the three securities is their time to maturity. The Treasury bond is redeemable in 10 years from today whereas Treasury note A is redeemable in 3 years and Treasury note B is redeemable in 5 years from today, respectively. Obtain their change in price if their yield to maturity (assumed to be 6.0% for all the three bonds) changes by 100 basis points (i.e., increases to 7% or decreases to 5%). Do all the bonds have the same change in price?