$1)$ Consider a two$-$period binomial share price model. Let the current share price be $$100$ and the appropriate risk$-$free rate be $4\%$ per period. Across a period, the share price can either increase by $8\%$ or decrease by $8\%.$ The share does not pay dividends.

a$)$ Find the current price of an at$-$the$-$money European style put option on the shares. Illustrate your answer using a diagram of the two$-$period binomial tree.