A stock currently sells for $50. In six months it will either rise to $60 or decline to $45. The continuous compounding risk-free interest rate is 5% per year.

1. Using the binomial approach, find the value of a European call option with an exercise price of $50.
2. Using the binomial approach, find the value of a European put option with an exercise price of $50.
3. Verify the put-call parity using the results of Questions 1 and 2.