You purchased a 30-year T-bond with a coupon rate of 2.25%, paid semi-annually, on February 15, 2022. The bond matures on January 20, 2047. The residual term to maturity is 24.929268 years.

a) You paid a clean price of 97.603114 percent of face value on February 15. What is the yield to maturity of this bond (in percent)?

b) The coupon payments on the bond you purchased on February 15 are made on January 20 and July 20. Calculate the dirty price (= clean price + accrued interest) as a percentage of face value of this bond at the time of purchase.