need help. How did they get all of these answers? This is to help me study for my test

4. A stock's price is $50. Over each of the next two three month periods it is expected to go up by 10% or down by 10%. The risk free rate is 4% p.a. The stock pays a dividend of $1 per quarter. Assume the option expires the day after the second period dividend is paid. a. What should be the current price of a 6-month European style put option with a strike price of $50 ? b. What should be the current price of a 6-month American style put option with a strike price of $50 ? c. What should be the current price of a 6-month European style call option with a strike price of $50 ? d. What should be the current price of a 6-month American style call option with a strike price of $50 ? 4. A stock's price is $50. Over each of the next two three month periods it is expected to go up by 10% or down by 10%. The risk free rate is 4% p.a. The stock pays a dividend of $1 per quarter. Assume the option expires the day after the second period dividend is paid. a. What should be the current price of a 6-month European style put option with a strike price of $50 ? b. What should be the current price of a 6-month American style put option with a strike price of $50 ? c. What should be the current price of a 6-month European style call option with a strike price of $50 ? d. What should be the current price of a 6-month American style call option with a strike price of $50