Use Two$-$State Binomial Option $($European$)$ Pricing Model.

Suppose you bought a stock today for $$20\mathrm{.}00.$

The stock price can either go up to $$23\mathrm{.}00$ or down to $$18\mathrm{.}00$ with equal probability in $0\mathrm{.}25$ years $($or $90$ days$).$

Suppose the annual risk$-$free rate is $8\mathrm{.}00\%$ and the option exercise price is $22\mathrm{.}00.$

How much should be the Call Option Value that expires in $0\mathrm{.}25$ years $($or $90$ days$)?$

Enter your answer in the following format: $0\mathrm{.}1234$

Hint: The answer is between $0\mathrm{.}4111$ and $0\mathrm{.}5224$