The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $52 that expires in 24 months. Each step is 1 year, the risk free rate is 5% per annum (continuously compounding), and the volatility is 30%. What is the option price? Show work in detail and use a tree diagram (Use 4 decimal places).