In May 2021, the U.S. Treasury issued 30-year bonds with a coupon rate of 6.25%, paid semi-annually. A bond with a face value of $1,000 pays a semi-annual coupon payment every six months for the next 30 years. (a) What is the value of the bond if, immediately after issue in May 2021, the 30-year interest rate increases to 7.5%? (b) What is the value of the bond if, immediately after issue in May 2021, the 30-year interest rate decreases to 5.0%? (c) On a graph show how the value of the bond changes as the interest rate changes (plot the value as a function of the interest rate). (d) At what interest rate is the value of the bond equal to its face value of $1,000