a$.$ Suppose that a stock has current price of $$15.$ It is expected that in $4$ months, the value of the stock would either be $$20$ or $$13.$ A $4$ months call option with strike price of $$17$ on the stock is being initiated today. If the interest rates are $5\%$ per annum for $4$ months continuously compounded then, what is the price of the call option today?

b$.$ What is the price of the option if it$$s a $4$ months put option with strike price $$18?$