A call option on a stock is trading for $$30$ per share with a $$32$ exercise price. The

stock's standard deviation is $36\%$ per year; the option matures in $6$ months; and

the risk$-$free interest rate is $4\%$ per year. Use the Binomial Model:

a$)$ Find the risk neutral probability assuming $3$ months for each step. $6$ points

b$)$ Find the call price $6$ points

c$)$ Find the put price?