Shares of Bluumberry & Co are currently trading at $45$ per share with volatility of $20\%.$ The share is expected to pay a dividend of $5$ in $2$ months$$ time. The risk$-$free rate of interest in

the economy is $5\%.$

Calculate the price of a call option if it is American$-$style using the binomial tree method with an exercise price of $47$ and maturity of $3$ months.