Consider a one$-$year call option that gives the holder the right but not the obligation to buy $100$ shares of a stock currently trading at $$50$ per share for $$48$ per share. By year$-$end the stock can increase to $$55/$share or decrease to $$45$ per share The risk free rate is $2\mathrm{.}00\%.$

Calculate the value of this call today within $$1$