One share of Sass & Fox Inc. is currently trading at $$30$ per share. In one year, the price is expected either $(1)$ rise to $$55$ or $(2)$ fall to $$10.$ You are interested in purchasing a call option on the stock. The option has a strike price of $$38$ and expires in $1$ year. The current risk$-$free rate for the year is $3\%.$

Based on binomial options pricing $($as shown in class$),$ what is a fair price for this option? Answer to the nearest cent, with no punctuation. That is$,$ $$5\mathrm{.}289$ should be entered as $"5\mathrm{.}29".$