Please answer all parts and show all work! Thank you! (Final assignment of college)

7. A stock sells, currently, for $100. Over each of the next 6-month periods it is expected to go up by 20% or down by 10%. The risk-free APR is 12% with monthly compounding. The stock is not expected to pay any dividends for at least one year. (a) What is the current price of a European put option on this stock with a strike price of $100 that expires in 1 year? (b) What is the current price of an American put option on this stock with the same strike price and expiration date as the European option? Will this put option be exercised early? If so, when