We present a model of the relationship between real interest rates, credit spreads, and the structure and risk of the banking system. Banks intermediate between entrepreneurs and investors, and can monitor entrepreneurs' projects. We characterize the equilibrium for a fixed aggregate supply of savings, showing that safer entrepreneurs will be funded by nonmonitoring banks and riskier entrepreneurs by monitoring banks. We show that an increase in savings reduces interest rates and spreads, and increases the relative size of the nonmonitoring banking system and the probability of failure of monitoring banks. We also show that the dynamic version of the model exhibits endogenous boom and bust cycles, and rationalizes the existence of countercyclical risk premia and the connection between low interest rates, tight credit spreads, and the buildup of risks during booms.