You are attempting to value a put option with an exercise price of $$109$ and one year to expiration. The underlying stock pays no dividends, its current price is $$109,$ and you believe it has a $50\%$ chance of increasing to $$127$ and a $50\%$ chance of decreasing to $$91.$ The risk$-$free rate of interest is $10\%.$ Calculate the value of a put option with exercise price $$109.$

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