You are analyzing stock XYZ. The current price of the stock is $110. A one-year European call option on XYZ with a strike price of $110 trades for $15, while a one-year European put option on XYZ with a strike price of $110 trades for $5.

Question 1: Use these prices to figure out the interest rate consistent with no arbitrage. (Using put-call parity)

Question 2: You are now tasked to price a binary put option. A binary put option with strike price $120 pays exactly $1 if the stock price is less than or equal to $120 and pays nothing if the stock price is above $120. A binary call option with strike price $120 pays exact $1 if the stock price is above $120 and pays nothing if the stock price is less than or equal to $120. You see that a binary call option on XYZ with strike price $120 is trading for $0.51. Use a no arbitrage relation to find the price of a binary put option on XYZ with strike price $120. Hint: these are not the standard options discussed so the standard put-call parity formula will not hold here. However, see if you can form a no-arbitrage relation that links the price of a binary call, binary put, and one or more other assets.