A normative framework for computing loan-Level and outstanding weighted interest rates in banking

Weighted average interest rates are central indicators in banking and financial analysis. They provide a coherent description of outstanding balances at the aggregate level but offer limited insight into how individual loans contribute to overall outcomes when exposures are heterogeneous. This paper introduces a normative framework that enables the construction of loan-level weighted interest rates while preserving exact consistency with outstanding balance aggregation. The approach is based on the explicit definition of a reference norm — the average exposure — which allows contractual rates to be transformed into structurally comparable measures. Within this framework, each loan’s weighted rate can be interpreted as a normalized contribution to outstanding balance interest income. A key result is that the arithmetic mean of loan-level weighted rates reproduces exactly the classical weighted average rate of the outstanding balance, ensuring full micro–macro coherence. An empirical illustration demonstrates the equivalence of several computational formulations and shows that, unlike nominal rates, weighted rates generate rankings that coincide with actual economic contributions. Beyond banking, the framework applies to any domain in which rates are computed over heterogeneous populations. The contribution of the paper is therefore methodological: it clarifies how interpretation can be improved without altering official aggregates. Keywords Weighted interest rates; Outstanding balance aggregation; Micro–macro consistency; Statistical normalization; Loan-level analysis; Heterogeneous exposures; Decomposition of rates; Financial indicators.