In this paper, we analyze the relation between interest rate targets and money supply in a (bubble-free) rational expectations equilibrium of a standard cash-in-advance model. We examine lump-sum injections of money aimed to implement interest rate sequences that satisfy interest rate target rules. An interest rate target with a positive inflation feedback in general corresponds to money growth rates rising with inflation. When prices are not completely flexible, this implies that a non-destabilizing money supply cannot implement a forward-looking and active interest rate rule. This principle also applies for an alternative model version with an interest elastic money demand. The implementation of a Taylor-rule then requires money injections that lead to explosive or oscillatory equilibrium sequences. In contrast, an inertial interest rate target can be implemented by a non-destabilizing money supply, even if the inflation feedback exceeds one, which is often found in interest rate rule regressions.