You are attempting to value a put option with an exercise price of $105 and one year to expiration. The underlying stock pays no dividends, its current price is $105, and you believe it has a 50% chance of increasing to $127 and a 50% chance of decreasing to $83. The risk-free rate of interest is 10%. Calculate the value of a put option with exercise price $105. (Do not round intermediate calculations. Round your answer to 2 decimal places.) (SHOW YOUR WORK PLEASE)