The common stock of the ABC Corporation has been trading in a narrow range, around $50 per share for months, and you believe it is going to stay in that range for the next three months. The price of a 3-month put option with an exercise price of $50 is $4.

(i) if the risk-free rate is 10% per year, what must be the price of a 3-month call option on ABC stock at an exercise price of $50 if it is at the money? (Assume put-call parity holds and the stock pays no dividend).

(ii) What would be a simple option strategy using a put and call to exploit your conviction about the stock price's future movements? Explain.

(iii) How far can the stock price move in either direction before you lose money?