Assume the current stock price of Apple is $500. The stock price will either increase by 10% or decrease by 10% in the first month. If the price increases in the first month, it will go up by $100 or down by $75 in the second month. If the price decreases in the first month, it will go up by 10% or down by 10% in the second month. The risk-free interest rate is 5% per month. Assume there is a 2-month put option with an exercise price of $500.

a) Use the replicating portfolio approach to calculate the value of the put if stock price increases in the first month.

b) Use the risk neutral probability approach to calculate the value of the put if stock price decreases in the first month.

c) Use either approach to calculate the 2-month put premium today.