The price at t = 0 of 1 share of a stock is $40.00. The annual discount rate (APR) is 4%. One year from now, one share of it will be $35 per share in the DOWN state and $45 per share in the UP state. What is the price today (at t = 0), of a PUT option with strike price of $40 and maturity (expiration) of 1 year? Please show your work.

What is the price of a CALL option with the same strike price ($40) and the same maturity (1 year)? Please show your work.