To study implications of an interest-bearing CBDC on the economy, we integrate a New Monetarist-type decentralised market that explicitly accountsfor the means-of-exchange function of bank deposits and CBDC into a NewKeynesian model with financial frictions. The central bank influences thestore-of-value function of money through a conventional Taylor rule while itaffects the means-of-exchange function of money through CBDC operations.Peak responses to monetary policy shocks remain similar in the presence of aninterest-bearing CBDC, implying that monetary transmission is not impaired.At the same time however, the provision of CBDC helps smooth responsesto macroeconomic shocks. By supplying CBDC, the central bank contributesto stabilising the liquidity premium, thereby affecting bank funding conditionsand the opportunity costs of money, which dampens and smoothes the reactionof investment and consumption to macroeconomic shocks.