We set up a model of banks, the central bank, the payment system, and the surrounding private sector economic environment. It is a structural, choice-theoretic model which is deeply rooted in data. We use the model to conduct a structural counterfactual that introduces a Central Bank Digital Currency (CBDC) which is optionally interest-bearing. The model can be used to provide estimates of the emerging CBDC-in-total-money shares, the drop of deposit rate spreads to policy rates, the impact on reserve needs, the implied rotation of profits away from banks toward central banks, and the extent to which monetary policy pass-through may become stronger. We obtain upper bound estimates for the CBDC-in-money shares of about 25 percent and 20 percent, respectively for the U.S. and euro area, when CBDC would be remunerated at the policy rates and be perceived as “deposit-like” by the public. Actual take-up may likely be below such upper bound estimates. The model codes—to replicate all results and to apply them to other countries—are made available along with the paper.