MATHEMATICAL ANALYSIS OF BANK DEPOSITS AND INVESTMENT GROWTH USING DIFFERENTIAL EQUATIONS

This article investigates the application of differential equations in the mathematical analysis of bank deposits and investment growth. Financial processes such as deposit accumulation, capital investment, and interest generation are dynamic phenomena that evolve continuously over time. Differential equations provide an effective mathematical framework for describing these processes and evaluating their long-term behavior. The study examines the relationship between deposit growth, investment returns, interest rates, and capital accumulation through mathematical models. Particular attention is given to continuous compound interest models and investment growth functions that are widely used in banking and financial analysis. The research demonstrates how differential equations can be employed to forecast future financial outcomes, optimize investment strategies, and assess the impact of changing economic conditions on capital growth. The findings indicate that mathematical modeling based on differential equations is a valuable tool for understanding financial dynamics and supporting informed decision-making in banking and investment management. Furthermore, the study highlights the practical significance of mathematical methods in evaluating long-term financial sustainability and economic development.