This paper studies how the impact of monetary policy depends on the distribution of savings from refinancing mortgages. We show that the efficacy of monetary policy is state dependent, varying in a systematic way with the pool of potential savings from refinancing. We construct a quantitative dynamic life-cycle model that accounts for our findings and use it to study how the response of consumption to a change in mortgage rates depends on the distribution of savings from refinancing. These effects are strongly state dependent. We also use the model to study the impact of a long period of low interest rates on the potency of monetary policy. We find that this potency is substantially reduced both during the period and for a substantial amount of time after interest rates renormalize.