You are attempting to value a put option with an exercise price of $$108$ and one year to expiration. The underlying stock pays no dividends, its current price is $$108,$ and you believe it has a $50\%$ chance of increasing to $$123$ and a $50\%$ chance of decreasing to $$93.$ The risk$-$free rate of interest is $10\%.$ Calculate the value of a put option with exercise price $$108.$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.