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 $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum (continuously compounding), and the volatility is 20%. What is the option price? Show work in detail and use a tree diagram (Use 4 decimal places).