A Novel Computational Framework for Annuity Interest Rate Determination: Beyond Traditional Interpolation Methods
Asuelinmen, Osoria *
Department of Basic Sciences, School of General Studies, Auchi Polytechnic, Auchi, Edo State, Nigeria.
Aliu Khalumele Ann
Department of Basic Sciences, School of General Studies, Auchi Polytechnic, Auchi, Edo State, Nigeria.
Bala Adamu
Department of Basic Sciences, School of General Studies, Auchi Polytechnic, Auchi, Edo State, Nigeria.
Onwuaru Patience
Department of Basic Sciences, School of General Studies, Auchi Polytechnic, Auchi, Edo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Aims: This study aims to develop a computationally efficient mathematical framework for determining the periodic interest rate in annuity contracts, thereby addressing the limitations of traditional tabular interpolation methods.
Study Design: The study employs mathematical derivation and numerical analysis to formulate the annuity interest rate problem as a root-finding exercise and implements the Newton-Raphson method with strategic initialisation and rigorous error quantification.
Place and Duration of Study: Department of Basic Sciences, School of General Studies, Auchi Polytechnic, Auchi, Edo State, Nigeria, between December 2025 and July 2026.
Methodology: The research derives the implicit nature of annuity equations from first principles, establishes rigorous bounds for the interest rate, and implements a Newton-Raphson algorithm with strategic initialisation and fallback strategies. A comprehensive error analysis, including truncation error, round-off error, convergence assessment, and sensitivity analysis, is conducted. The framework is extended to handle frequency mismatches, deferred payments, and variable payment schedules. A MATLAB implementation is provided for practical application. All numerical experiments were performed using MATLAB R2023a with a consistent stopping tolerance of .
Results: The proposed algorithm achieves convergence in 3-5 iterations, compared with 10-15 iterations required by interpolation methods. Truncation error after 5 iterations is less than , while round-off error is bounded by . The methodology demonstrates an approximately 85-90% reduction in computational operations compared to conventional table-based approaches under identical numerical conditions.
Conclusion: The proposed computational framework provides an efficient, accurate, and transparent methodology for annuity interest rate determination, eliminating reliance on pre-computed reference tables. The framework is suitable for real-time financial applications across banking, investment, and insurance sectors.
Keywords: Annuity interest rate, computational finance, Newton-Raphson method, numerical root finding, financial mathematics, error analysis, sensitivity analysis, strategic initialisation, deferred annuities, variable-payment annuities