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.) (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.)

Economy	probability	YTM	Price	Capital Gain	Coupon Interest	HPR
Boom	.25	7.0%
Normal Growth	.40	5.0%
Recession	.35	4.0%