Please provide step-to-step explanation, and round answers to 4 decimal places. Thank you.

DIY is trading at $550 per share. The stock price will either increase by 5% or decrease by 15% in the first month. If the price increases in the first month, it will go up by $120 or down by $180 in the second month. If the price decreases in the first month, it will go up by $45 or down by $60 in the second month. The risk-free interest rate is 5% per month.

a. Using the replicating portfolio approach, find the price of a 1-month put option that has an exercise price of $500.

b. Using the risk neutral probability approach, find the price of a 1-month call option that has an exercise price of $500.

c. Using either approach, find the price of a 2-month put option that has an exercise price of $500.