Mathematical Modeling of Business Growth Dynamics in the Banking Sector: The Role of Customer Acquisition, Conversion, and Retention
DOI:
https://doi.org/10.33003/fjs-2026-1016-5902Keywords:
Business Growth, Mathematical Modeling, Banking Sector, Customer Retention, Conversion Rate, Differential Equation, Churn Rate, Sustainable GrowthAbstract
In this paper, we provide a mathematical framework of business development in the banking industry, using three variables, namely, customer acquisition (L), conversion (C) and retention (M). The easiest formula to use is a basic core formula that indicates that growth is a product of these variables where a low score on any will drastically lower the overall performance. The equation is extended into a differential equation to be able to describe the time-dependent development of the customer base with references to the growth and loss (churn) of the customer base. Numerical solution shows that acquisition and conversion can be added to the growth linearly, whereas retention can be added to the sustainability of growth much more significantly. The results highlight that enhancing customer retention by virtue of enhancing service delivery is the most crucial determinant of business growth that is long term and which is therefore most important in profitability and the stability of the organization.
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Copyright (c) 2026 William Atokolo, Remigius Okeke Aja, Joseph Egbemhenghe, Jeremiah Amos, David Omale
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