A stock currently priced at $$20,$ its annual volatility is $20\%$ and it will not pay any dividends in the near future. The risk free rate is $12\%.$ The following are option with three months to maturity. Price the options assuming monthly binomial steps $($three period steps$).$ No Excel.

a$.$ A call option with a strike of $$22$

b$.$ A European put option with a strike of $$22.$

c$.$ An American put option with a strike of $$22.$