A stock is currently $$70.$ Over each of the next twelve one$-$month periods $($this is a $12-$step binomial tree$),$ it is expected to go up by $3\%$ or down by $3\%.$ The risk$-$free rate is $5\%$ per annum with continuous compounding for all maturities. Value a one$-$year European call with a strike price of $$55.$

please show all of your work and provide the answer.