Modeling Real-Value Preservation in Retirement Planning via Geometric Progressions: An Applied Math Perspective

This paper proposes a mathematical model based on modified geometric progressions for supplementary retirement planning. Unlike traditional annuity models that assume fixed contributions and withdrawals, the proposed method incorporates inflation-indexed contributions and withdrawals. This allows for accurate simulations aligned with real-world financial behavior. The model has practical applicability in pension fund policy, personal financial planning tools, and governmental simulations. A case study is developed, demonstrating that with a 3% annual geometric annuity and a 0.5% monthly interest rate, an initial deposit of R$ 767.67 over 25 years results in a monthly retirement income of R$ 3049.19 for 30 years, with preserved purchasing power. The model offers a practical and realistic tool for individual retirement planning and paves the way for future applications in both public and private pension systems.