Generally, the geometric Brownian motion (GBM) efficiently models financial instruments with constant drift and volatility, while the Milstein scheme refines the simulation, particularly in the case of high volatility or large time steps. In this work, the Milstein scheme is initially utilized to discretize the solution process for the GBM model. Subsequently, the maximum-likelihood estimation method is applied to derive analytical formulas of the parameter estimators. Using relative absolute errors and R software, it is established that, under reasonable condition, the parameter estimators of the process​ converge to their true values. More importantly, the paper further illustrates the practical use of the GBM process through modeling Morocco’s real interest rates (IRs), considering the absolute errors of the estimators and reinforced by numerical simulations. The findings offer significant insights for predicting the future dynamics of Morocco’s real IRs over the next four years.