We develop a quantitative New Keynesian DSGE model to study the introduction of a central bank digital currency (CBDC): government-backed digital money available to retail consumers. At the heart of our model are monopolistic banks with market power in deposit and loan markets. When a CBDC is introduced, households benefit from an expansion of liquidity services and higher deposit rates as bank deposit market power is curtailed. However, deposits also flow out of the banking system and bank lending contracts. We assess this welfare trade-off for a wide range of economies that differ in their level of interest rates. We find substantial welfare gains from introducing a CBDC with an optimal interest rate that can be approximated by a simple rule of thumb: the maximum between 0% and the policy rate minus 1%.