You are attempting to value a put option with an exercise price of $$102$ and one year to expiration. The underlying stock pays no dividends, its current price is $$102,$ and you believe it has a $50\%$ chance of increasing to $$121$ and a $50\%$ chance of decreasing to $$83.$ The risk$-$free rate of interest is $5\%.$ Calculate the value of a put option with exercise price $$102.($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Value of a put option