Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% 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 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.) Economy Boom Normal Growth Recession Probability 0.10 0.60 0.30 YTM 9.0 % 8.0 % 7.0 % Price Capital Gain Coupon Interest HPR % % %