A European put option has an exercise price of 100. It has one year to expiration. The underlying stock does not pay any dividends and has a current price of 90. This price has a 50% chance of increasing to 110 and a 50% chance of decreasing to 70. The risk free rate of interest is 1% p.a. Calculate the price of the put option using the two state stock price model applying the replicating portfolio method.