A stock is trading at $$300$ with a volatility of $0\mathrm{.}5.$ The risk free rate is $5\%.$ The stock does not pay dividends. Create a $2-$step tree for the stock with a time step of $1$ year.

What is the price of a derivative contract that pays you $$300$ if the stock is above $$300$ and pays $$20$ if the stock is below $($or equal to$)$ $$300.$

$$303\mathrm{.}73$

$$82\mathrm{.}38$

$$56\mathrm{.}34$

$$64\mathrm{.}23$