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.)

\begin{tabular}{|l|r|r|r|r|r|l|l|} \hline \multicolumn{1}{|c|}{ Economy } & Probability & \multicolumn{2}{|c|}{ YTM } & Price & Capital Gain & CouponInterest & \multicolumn{1}{|c|}{} \\ \hline Boom & 0.30 & 10.0 & % & & \\ \hline Normal Growth & 0.40 & 8.0 & % & & \\ \hline Recession & 0.30 & 6.0 & % & & \\ \hline \end{tabular}