The price of a stock today is $$70.$ In $12$ months, the stock may go up to $$80,$ or it may fall to $$64.$ The risk$-$free rate is $4\%$ per year. What is the arbitrage$-$free price of a call option that expires in $12$ months and has a strike price of $$75?$

Group of answer choices

$$6\mathrm{.}97$

$$2\mathrm{.}64$

$$1\mathrm{.}08$

$$1\mathrm{.}88$