Work

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

Year: 2025

Type: article

Abstract: 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.

Source: AppliedMath

DOI: 10.3390/appliedmath5030110

Authors: Ana Kerma Araujo Gomes de Sousa, Kailany de Medeiros Nóbrega, Anderson Felipe Tiburcio, Fábio Sandro dos Santos, Evádio Pereira Filho, Fernando Henrique Antunes de Araujo

Institutions: Instituto Federal de Educação Ciência e Tecnologia da Paraíba, Universidade Federal do Piauí

Language: English

Topic: Financial Literacy, Pension, Retirement Analysis

Subfield: Accounting

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,207

Funder: Conselho Nacional de Desenvolvimento Científico e Tecnológico