Use the binomial method to determine the value of an American Call option at time $t=0.$ The option expires at time $t=T=1$ and has exercise price $E=100.$ The current value of the underlying is $S(0)=100$ with the underlying paying continuous dividends at the rate $D=0\mathrm{.}2.$ The interest rate is $r=0\mathrm{.}05.$ Use a time step of $t=\frac{1}{3}.$ Consider the case of $p=\frac{1}{2}$ and suppose the volatility is $=0\mathrm{.}4.$ Perform all calculations using a minimum of $4$ decimal places of accuracy.