Mathematical Analysis of Loan Repayment Schedules and Interest Accumulation in Nigerian Microfinance Banks

This study analyses the mathematical structure of loan repayment schedules and interest accumulation in microfinance banks operating in Nigeria, with case study data drawn from three licensed microfinance institutions in Akure, Ondo State, South West Nigeria. Microfinance lending has been positioned by the Central Bank of Nigeria as a key instrument for financial inclusion, poverty alleviation, and small enterprise development, yet borrowers frequently lack the financial literacy to evaluate the true cost of credit products. The study constructs amortisation schedules for representative loan products offered by the sampled institutions, computing total interest payments, effective annual interest rates, and outstanding principal balances at each repayment period under flat rate, declining balance, and graduated repayment structures. Comparison of nominal interest rates advertised by lenders against computed effective annual rates reveals substantial discrepancies, with effective rates in some flat-rate products exceeding twice the advertised rate. The impact of loan tenor, repayment frequency, and compounding convention on total borrower cost is explored through parametric sensitivity analysis. The study further examines the mathematical conditions under which early loan repayment generates net savings for borrowers given prepayment penalty clauses. Findings are contextualised within the financial literacy research literature for sub-Saharan Africa. The study recommends the mandatory disclosure of effective annual interest rates in all loan contracts, consistent with the CBN's consumer protection framework. Keywords: loan repayment, amortisation, interest accumulation, microfinance, financial mathematics