Consider an european call option on a stock that is not paying dividends with the following characteristics.

$($i$)$ The stock price at $t=0$ is $S=$$$30.$

$($ii$)$ The stricke price is $$31.$

$($iii$)$ The volatility of the stock is $20\%.$

$($iv$)$ The free risk interest rate is $7\%.$

Construct a $2$ period recombining Binomial tree diagram and spec$$y tne varue or tne can optron at eacn node of the tree diagram.