You are attempting to value a put option with an exercise price of $$107$ and one year to expiration. The underlying stock pays no dividends, its current price is $$107,$ and you believe it has a $50\%$ chance of increasing to $$125$ and a $50\%$ chance of decreasing to $$89.$ The risk$-$free rate of interest is $8\%.$ Calculate the value of a put option with exercise price $$107.$

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

Value of a put option