$1)$ A stock has a beginning market value of $$80.$ It can either increase in value each year by $15\%$ or decrease in value by $15\%.$ A $3-$year European call option written on the stock has an exercise price of $$80.$ The risk$-$free rate of return is $5\%$ per years. What is the current equilibrium price of the call option if you maintain a riskless portfolio by readjusting your relative positions in stocks and puts at the end of each year? Please draw both the stock and option tree. Please operate with $2$ decimals and show all work