This system models the stock price of a bank using Geometric Brownian Motion(GBM) with a deterministic seasonal initial condition. The Stochastic Differential Equation (SDE) is formulated to capture annual dividend, earnings, and macroeconomic cycles in the Nigerian banking sector. Three sample paths are simulated examines the future share price dynamics of First Bank under a seasonal Stochastic Differential Equation (SDE) framework using three figures. The analysis considers stochastic Brownian paths, deterministic seasonal cycles, and sensitivity to amplitude parameter A.  Results show that while seasonality drives recurring patterns, random shocks and amplitude changes determine short-term dispersion and volatility. Under Lipschitz and linear growth conditions, existence and uniqueness of a strong solution is proved via Itô’s Lemma, yielding. To this end, the model provides a framework for timing entry and exit around quarterly results.