The current price of a non-dividend paying stock is $100. Over each of the next two 3-month periods, the stock price is expected to either move up by 10% or move down by 10%. The risk-free rate is 12% per annum with continuous compounding. Using a two-step binomial model, what is the value today of an American put option on the stock with a strike price of $101 and a time to maturity of 6 months?