According to the February $7,1983,$ issue of the Sporting News, the Kansas City Royalsdesignated hitter, Hal McRae, signed a three$-$year contract in January $1983$ with the following provisions: $$400,000$ signing bonus. $$250,000$ salary per year for three years. $10$ years of deferred payments of $$125,000$ per year $($these payments begin in year $4).$ Several bonus provisions that total as much as $$75,000$ per year for the three years of the contract. Assume that McRae has a $60\%$ probability of receiving the bonuses each year, and that he signed the contract on January $1,1983.($Hint: Use the expected bonuses as incremental cash flows$).$ Assume an effective annual rate of interest of $12\mathrm{.}36\%$ and ignore taxes. McRaes salary and bonus are paid at the end of each year. What was the present value of the contract in January when McRae signed it$?$