At t = 0, the price of a certain stock is S(0) = $50. At t = 1, the price is either S(1) = $80 or S(1) = $30. A certain option contract is worth $10 if the stock price is $80, and is worth $0 if the stock price is $30. Assuming no arbitrage opportunities, and continuously compounded interests of 5%, what is the price of the option at time t = 0?