Two models by Garnett et al. [J. Bus. Hist. 57(1):182-202 (2015)] for the organisational demography of British banks are explored analytically: the exponential model; and the agent-based system (ABM) governed by probabilistic interactions. Exact expressions for ABM expectation values are derived, revealing first that bank creations obey a ‘birth’ process, and second, that one of the ABM hypotheses may be discarded. The expectation values are used to demonstrate that beneath its stochastic implementation, the ABM model is a discrete analogue of the exponential model, meaning that the decline in the British bank population obeys a law of negative compound interest.