There is an American put option on a stock that expires in two months. The stock price is $69 and the standard deviation of the stock returns is 59 percent. The option has a strike price of $78 and the risk-free interest rate is an annual percentage rate of 5.8 percent.

What is the price of the option? Use a two-state model with one-month steps. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)