Consider a European put option on the Apple (AAPL) stock that matures in 6 months. The current price of AAPL stock is $176 and the put option is priced at-the-money (i.e. the strike price of this option is also $176). The volatility of AAPL is 33% per annum and the risk-free rate is 1%. Use the two-period binomial model:

1. Calculate u, d and the risk neutral probability (show details of your calculations using regular formulas).
2. Construct and present here the two-period binomial three for the stock price of AAPL.
3. Find payoffs of the option at expiration
4. Find the price of this put option (show regular, not excel formulas and how you plugged numbers into them.)