Consider a stock that is currently trading at $50 and has an annualized volatility of 30%. The stock is not expected to pay any dividends in the next 3 months. The annualized risk-free rate is 4%.

1. Calculate the Black-Scholes price of a cash-or-nothing binary call option that matures in 3 months. The option pays nothing if the stock price at maturity is less than $40, and pays a fixed amount of $40 if the stock price at maturity is higher than $40.

2. Calculate the Black-Scholes price of an asset-or-nothing binary call option that pays nothing if the stock price at maturity (3 months) is less than $40, and pays the value of the stock price at maturity (or delivers the stock) if the stock price at maturity is higher than $40.

3. Use your answers from parts (A) and (B), and only your answers from parts (A) and (B) to find the Black-Scholes price of a European call option on the same underlying stock that matures in 3 months and has a strike price of $40. Please explain your answer carefully.