$5.$ Given: Today's stock price is $37.$ One month from now, the stock price will be either $35$ or $40.$ If it is $35,$ then the following month the stock price will be either $31$ or $37.$ If it is $40$ one month from now, then the following month the price will be either $37$ or $45.$ The risk$-$free rate of interest is $1\%$ per month. How much should one be willing to pay today for a call option on the stock with K $=35$ and T $=2$ months? Construct the binomial tree for a European call option. At each node, provide the call premium $($i$.$e$.,$ value$)$ as well as $\backslash$Delta and B$.$