The price of a firms stock is currently $50 per share. The stock price follows a binomial process where it either goes up 20% or down 20% each year. The stock pays no dividends, and the risk-free interest rate is 2% each year. Consider an American put option on the stock with a strike price of $50 and 2 years to expiration.

3a) Suppose that the stock price goes up 20% in the next year to $60 per share in 1 year. What is the value of the put option at that point assuming that the option is not exercised until expiration (i.e., until the end of the following year, when the stock price could go up to $72 or down to $48)?