Consider a put option with $50 strike price and maturity equal to 1 year. The underlying stock price is $40 and the volatility of the stock is 25%. The stock is not expected to pay any dividends within the next year. The risk-rate of return is 5%.

1. Calculate the value of u, d, and the risk-neutral probability p for a two-step tree.

2. Using the Binomial tree approach, find the price of a European put option.

3. What would the price of the option be if it were instead American in nature?

Please show all necessary steps