You use the following information to construct a binomial forward tree for modeling the price movements of a stock:

(i) The length of each period is 4 months.

(ii) The current stock price is 55.

(iii) The stock’s volatility is 30%.

(iv) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3.5%.

(v) The continuously compounded risk-free interest rate is 5%.

Calculate the price of a 1-year 50-strike American put option on the stock.