Consider a stock currently trading at $100. A manager is considering to buy a 2-year at-the-money put option on the stock. For the valuation of this put option, the manager has selected binomial method for the valuation. The periodically compounded interest rate is 3% and the stock is expected to increase by 25% in case if it moves up. 

Calculate the value of a two-period European-style put option on the stock that has an exercise price of $50. Also, determine if early exercise after 1-year at $105 would make economic sense.