Several studies have recently adopted the segmented markets model as a framework for monetary analysis. The characteristic assumption is that some households never participate in financial markets. This paper proves the existence of an equilibrium for segmented markets models where monetary policy is defined in terms of the short-term nominal interest rate. The model allows us to consider the important cases where monetary policy affects output, and responds to any sources of uncertainty, including output itself. The assumptions required for existence constrain the maximum value and the variability of the nominal interest rate. The period utility function is logarithmic. The proof is constructive, and shows how the model can be solved numerically. A similar proof can be used in the case that monetary policy is defined in terms of the bond supply.