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Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a...

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%
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