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 "O" 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 Probability YTM Price HPR Boom 0.25 7.0 % $ 39.45 x $ Capital Coupon Gain Interest (60.55) $ 4.00 x (50.99) $ 4.00 (36.83) X $ 4.00 X Normal Growth 0.40 5.0 % 49.01 X $ (56.55) X % (46.99) X % (32.83) X % Recession 0.35 4.0 % $ 63.17 X $