Suppose that the current Bitcoin futures price is $$60,000,$ and the risk free rate is $5\%$ per annum $($with continuous compounding$).$ What is the lower bound of the value of a six$-$month put option on one Bitcoin futures contract with a strike price of $$62,500?($Hint: assume each futures contract represents one unit of the underlying asset, and express your answer in dollar term to the nearest cent.$)$