We investigate the welfare-increasing role of credit and banking at zero interest rates in a microfounded general equilibrium monetary model. Agents differ in their opportunity costs of holding money due to heterogeneous idiosyncratic time-preference shocks. Without banks, the constrained-efficient allocation is never attainable, since impatient agents always face a positive implicit rate in equilibrium. With banks, patient agents pin down the borrowing rate and in turn enable impatient agents to borrow at no cost when the inflation rate approaches the highest discount factor. Banks can therefore improve welfare at zero rates, provided that both types of agents are included in the financial system and that the borrowing limit is sufficiently lax. The result is robust to several extensions.