$(8$ points$)$ The current price of Beach House Industries stock is $$40.$ In the next year the stock price will either go up by $10\%$ or go down by $5\%.$ Beach House pays no dividends. The one year risk$-$free rate is $2\%$ and will remain constant. Calculate the price of a one$-$year call option on Beach House stock with a strike price of $$55.$