This paper develops a small-scale DSGE model which embeds a demographic structure within a monetary policy framework. We extend the tractable, though non-monetary overlapping-generations model of Gertler (1999) and present a small synthesis model which combines the set-up of Gertler with a New-Keynesian structure, implying that the short-run dynamics related to monetary policy are similar to the paradigm summarized in Woodford (2003). In sum, the model offers a New-Keynesian platform which can be used to investigate in a closed economy set-up the response of macroeconomic variables to demographic shocks, similar to technology, government spending or monetary policy shocks. Empirically, we use a calibrated version of the model to discuss a number of macroeconomic scenarios for the euro area with a horizon of around 20 years. The main finding is that demographic changes, while contributing slowly over time to a decline in the equilibrium interest rate, are not visible enough within the time horizon relevant for monetary policy-making to require monetary policy reactions.