Consider a 6-month put with a strike price of $44 on a stock whose current price is $40. Assume that there are two-time steps, and in each time, step the stock price either moves by 10% or moves down by 10%. We also suppose that the risk-free rate of interest is 2%. Compute the value of the put using the recombining binomial tree under the assumption that the option is European and under the assumption that the option is American.