1. You Consider a stock with a price of $50 that is expected to increase by 6% or decrease by 8% each month over the next two months. Having a risk-free rate of 3% per year with continuous compounding, calculate the value of a two-month European put option with a strike price of $55. 
2. 
   
3. Repeat your calculations for a two-month American put option with a strike price of $55. Show clearly all your calculations and results with the use of the relevant equations and graphs. Discuss your investment decision in each case separately.