$1.$ Current Stock price S$(0)$ is $$60$; risk$-$free rate is $3\%($simple rate$).$ There are two possible outcome in one year, stock price might go up $40\%($to $$84)$ or go down $40\%($to $$36).$ Consider both a call and a put with the same strike price of $$60$ and one year to maturity.

a$.$ You estimate that the probability of stock price to go up is $90\%$ and probability to go down is about $10\%.$ Compute the price of call and put and also expected returns on the stock, call, put and a straddle $($combination of a call and put with same strike of $$60)$ using the binomial tree model. $(6)$