Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 3.5% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows: (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	0.25	12.0	%	$	$	$	%
Normal Growth	0.40	10.0	%	$	$	$	%
Recession	0.35	9.0	%	$	$	$	%