The aim of this study is to disentangle the effects of introducing an interest-bearing central bank digital currency (CBDC) for financial stability using a Diamond and Dybvig (1983) model in which (i) both CBDC and private bank deposits can be used in exchange and (ii) liquidity is created endogenously. Agents have direct access to a CBDC, which is a claim on the central bank. They use both sight deposits and CBDC to buy goods and commercial banks borrow reserves to cover liquidity needs. The introduction of an interest-bearing CBDC has direct implications for the sight deposit rate and the loan rate of banks. Besides, if the central bank aims to have a positive net worth and the absence of bank runs, a high demand for a CBDC is a necessary condition to achieve both objectives. If this is not the case, financial stability will be endangered.