The stock price of firm XYZ is currently $50. assume a stochastic differential equation of dSt = 0.04Stdt + 0.12StdWt under the real-world probability measure P, where Wt is a standard Brownian motion. The constant continuous dividend yield of firm XYZ is 1% per annum and the continuously compounded risk-free rate is 2.5% per annum.

Using 1000 simulation scenarios and equal sub-intervals of t = 1 2 year, estimate the mean of S5 for firm XYZ by discretizing the above SDE. Compare the estimated value with the theoretical expected value of S5 under measure P.