(15%) Under the assumptions of the BSM model, consider a binary option on a non-dividend paying stock with a strike price of $30 per share and one year to expiry. The stock's current price is $20 per share, its continuously compounded expected return (or growth rate) is 10% per annum, and its volatility is 20% per annum. Finally, the continuously compounded risk-free rate is 3% per annum. a) (5%) Calculate the current price of the binary option. b) (5%) Determine the real-world expected payoff on the binary option. Hint: The expected payoff of a binary option is the probability of the payoff event. c) (5%) Determine the binary option's real-world, continuously compounded expected return.