Problem 5-8 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.) Answer is complete but not entirely correct. Economy Price HPR Boom Probability 0.25 0.50 0.25 YTM 10.0 90 $ Capital Gain (60.55) (50.99) 136.83) R 39.45 49.01 63.17 $ $ S Normal Growth Recession Coupon Interest 4.00 400 4.00 (56.55) % (46.99) % (32.83) 3 % 80 $