We study optimal policy for a central bank that supplies interest-bearing central bank digital currency (CBDC) and reserves. We model a CBDC that competes with bank deposits as a medium of exchange. Monopolistic banks issue deposits to lend to productive investment projects. We show that CBDC leads to increased remuneration on bank deposits. CBDC promotes intermediation and increases bank profits for low to moderate interest rate levels. Setting the interest rate on CBDC equivalent to the Friedman rule, and offering the same interest rate on CBDC and reserves, is optimal if there is no risk on bankers’ balance sheet. If risk exists, the Friedman rule may lead to sub-optimal investment decisions and build-up of banking sector risk. If the CBDC rate is set higher than the optimal level, reserves become an important policy tool to crowd out sub-optimal investment and mitigate banking sector risk.