Problem $21-36($Algo$)$

You are attempting to value a call 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 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.

Answer is complete but not entirely correct.

Call option's value

$$,10\mathrm{.}00$