You are attempting to value a call 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 $10\%.$ Calculate the call option$$s value using the two$-$state stock price model.

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