For all problems where a risk free rate or a dividend yield is given, assume that the interest rate and the dividend yield are annual and continuously compounded rates.

Problem 4 The current price of the S&P 500 index is $3000. The volatility of the index is 30%, the risk-free interest rate is 3%, and the dividend yield is 2%. Using the Black-Scholes-Merton pricing framework (chapter 15.3 of the textbook), estimate today's probability that the index price will be less than or equal to $3000 in one year