Part 1.

The current price of a stock is $55. Calculate the value of an American put option on the stock using a two-step binomial tree given the following information.

The strike price of the option, K = $57, each time step is one year, the risk-free interest rate,

r = 5%, u =1.25, d = 0.8, and p = 0.6282

Part 2.

Given that u=e^(*T), calculate the implied volatility for the American put option in Part 1.