A stocks price today is S_o = 100. It is known that at the end of 6 months it will be either $120 or $80. The risk-free interest rate is r = 5% per annum with continuous compounding. We are interested in computing the todays price of a T = 6M month European Put and Call options on this asset with the same strike price K = 90 using a 1-step Binomial model.

Give the Put option payoff at maturity P_T as a function of the asset price at maturity S_T and use Risk- Neutral Pricing for the Put option to compute its price P₀ at time 0.

Give the Call option payoff at maturity C_T as a function of the asset price at maturity S_T and use Risk- Neutral Pricing for the Call option to compute its price C₀ at time 0.

I need step by step solution and formulas. Thank you.