This paper develops a small-scale DSGE model that embeds a demographic structure within a monetary policy framework. We extend the nonmonetary overlapping-generations model of Gertler and present a small synthesis model that combines the setup of Gertler with a New Keynesian structure, implying that the short-run dynamics related to monetary policy can be compared with that of the standard New Keynesian model. In sum, the model offers a New Keynesian platform that can be used to characterize the response of macroeconomic variables to demographic shocks, similarly to the responses to technology or monetary policy shocks. We offer such characterizations for flexible and sticky price equilibria. Empirically, we calibrate the model to demographic developments projected for the euro area. The main finding is that the projected slowdown in population growth and the increase in longevity contribute slowly over time to a decline in the equilibrium interest rate.