Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 4.0% couponif 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 4.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)

Economy	Probability	YTM		Price	Capital Gain	Coupon Interest	HPR
Boom	0.10	6.0	%	$	$	$	%
Normal Growth	0.60	5.0	%	$	$	$	%
Recession	0.30	4.0	%	$	$	$	%