Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 3.5% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 3.5% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.)

Economy	Probability	YTM		Price	Capital Gain	Coupon Interest	HPR
Boom	0.30	9.0	%					%
Normal Growth	0.50	7.0	%					%
Recession	0.20	5.0	%					%