Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya

Albert Ngiela; Mark Kimathi; Stanley Rotich

doi:doi:10.11648/j.acm.20261504.13

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Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya

Albert Ngiela^*

, Mark Kimathi

, Stanley Rotich

Published in Applied and Computational Mathematics (Volume 15, Issue 4)

Received: 23 June 2026 Accepted: 6 July 2026 Published: 21 August 2026

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Abstract

Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.

Published in	Applied and Computational Mathematics (Volume 15, Issue 4)
DOI	10.11648/j.acm.20261504.13
Page(s)	144-153
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2026. Published by Science Publishing Group

Keywords

Mathematical Modeling, MSMEs, Financial Literacy, Loan Repayment, Stability Analysis, Sensitivity Analysis

References

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[6]	Priyantoro, R., & Aisjah, S. (2023). The effect of financial literacy on MSME performance with financial inclusion as a mediating variable. International Journal of Research in Business and Social Science, 12(3), 214-224. https://doi.org/10.20525/ijrbs.v12i3.2147
[7]	Mwaniki, L. N. (2019). Financial literacy and growth of small and medium enterprises in Nyeri County, Kenya (Master's thesis, Kenyatta University).
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[9]	Gaudence, M., Patrick, M., & Denys, M. (2018). Effects of financial literacy on loan repayment among small and medium entrepreneurs of microfinance institutions: Case study of Inozamihigo Umurenge SACCO in Nyaruguru District. IOSR Journal of Business and Management, 20(5), 19-37. https://doi.org/10.9790/487X-20050341937
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APA Style

Ngiela, A., Kimathi, M., Rotich, S. (2026). Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Applied and Computational Mathematics, 15(4), 144-153. https://doi.org/10.11648/j.acm.20261504.13

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Ngiela, A.; Kimathi, M.; Rotich, S. Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Appl. Comput. Math. 2026, 15(4), 144-153. doi: 10.11648/j.acm.20261504.13

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AMA Style

Ngiela A, Kimathi M, Rotich S. Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Appl Comput Math. 2026;15(4):144-153. doi: 10.11648/j.acm.20261504.13

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@article{10.11648/j.acm.20261504.13,
  author = {Albert Ngiela and Mark Kimathi and Stanley Rotich},
  title = {Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {4},
  pages = {144-153},
  doi = {10.11648/j.acm.20261504.13},
  url = {https://doi.org/10.11648/j.acm.20261504.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261504.13},
  abstract = {Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.},
 year = {2026}
}

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TY  - JOUR
T1  - Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya
AU  - Albert Ngiela
AU  - Mark Kimathi
AU  - Stanley Rotich
Y1  - 2026/08/21
PY  - 2026
N1  - https://doi.org/10.11648/j.acm.20261504.13
DO  - 10.11648/j.acm.20261504.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 144
EP  - 153
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20261504.13
AB  - Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.
VL  - 15
IS  - 4
ER  -

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Author Information

Albert Ngiela

Department of Mathematics and Statistics, Machakos University, Nairobi, Kenya

Contact Email

http://orcid.org/0009-0001-4960-0352
Mark Kimathi

Department of Mathematics and Statistics, Machakos University, Nairobi, Kenya

http://orcid.org/0000-0002-5822-8687
Stanley Rotich

Department of Mathematics and Statistics, Machakos University, Nairobi, Kenya

http://orcid.org/0000-0001-8210-6586

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APA Style

Ngiela, A., Kimathi, M., Rotich, S. (2026). Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Applied and Computational Mathematics, 15(4), 144-153. https://doi.org/10.11648/j.acm.20261504.13

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ACS Style

Ngiela, A.; Kimathi, M.; Rotich, S. Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Appl. Comput. Math. 2026, 15(4), 144-153. doi: 10.11648/j.acm.20261504.13

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AMA Style

Ngiela A, Kimathi M, Rotich S. Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya. Appl Comput Math. 2026;15(4):144-153. doi: 10.11648/j.acm.20261504.13

Copy | Download

@article{10.11648/j.acm.20261504.13,
  author = {Albert Ngiela and Mark Kimathi and Stanley Rotich},
  title = {Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya},
  journal = {Applied and Computational Mathematics},
  volume = {15},
  number = {4},
  pages = {144-153},
  doi = {10.11648/j.acm.20261504.13},
  url = {https://doi.org/10.11648/j.acm.20261504.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20261504.13},
  abstract = {Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Qualitative Analysis of Financial Literacy and Loan Repayment Dynamics Among MSMEs in Kenya
AU  - Albert Ngiela
AU  - Mark Kimathi
AU  - Stanley Rotich
Y1  - 2026/08/21
PY  - 2026
N1  - https://doi.org/10.11648/j.acm.20261504.13
DO  - 10.11648/j.acm.20261504.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 144
EP  - 153
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20261504.13
AB  - Micro, Small and Medium Enterprises (MSMEs) play a significant role in employment, income generation and Gross Domestic Product (GDP) in Kenya, but many enterprises remain financially weak, carry heavy loan debt and struggle to repay. This study formulates a nonlinear ordinary differential equation (ODE) model to investigate the interaction between financial literacy, financial health, loan burden, cash reserves and stressors in the business environment for MSMEs in Kenya. The model provides a flexible tool for analysing the equilibrium behavior, positivity, boundedness, local stability and parameter sensitivity. The analysis shows that under economically sensible assumptions the model solutions are non-negative and bounded. An asymptotic stable equilibrium is constructed and calculated to be cash exhausted with the baseline parameter set and found to be locally stable. Sensitivity results show that financial efficacy and literacy intervention have positive effects on financial health, while literacy decay, debt-servicing and business stressors have negative effects on enterprise sustainability. The phase portrait and sensitivity visualization illustrate the financial-health--loan-burden trajectory and the relative influence of the principal model parameters. The study yields a mathematical framework for designing financial literacy programs, credit-management strategies, and interventions to support loan repayment that can help improve the resilience of MSMEs and their ability to repay loans.
VL  - 15
IS  - 4
ER  -

Copy | Download