We extend the New Keynesian Monetary Policy literature relaxing the assumption that the decisions are taken by a single policymaker, considering instead that monetary policy decisions are taken collectively in a committee. We introduce a Monetary Policy Committee (MPC), whose members have different preferences between output and inflation variability and have to vote on the level of the interest rate. This paper helps to explain interest rate smoothing from a political economy point of view, in which MPC members face a bargaining problem on the level of the interest rate. In this framework, the interest rate is a non-linear reaction function on the lagged interest rate and the expected inflation. This result comes from a political equilibrium in which there is a strategic behavior of the agenda setter with respect to the rest of MPC's members. Our approach can also reproduce both features documented by the empirical evidence on interest rate smoothing: a) the modest response of the interest rate to inflation and output gap, and b) the dependence on lagged interest rate, features that are difficult to reproduce altogether in standard New Keynesian models. It also provides a theoretical framework on how disagreement among policymakers can slow down the adjustment on interest rates and on "menu costs" in interest rate decisions. Furthermore, a numerical exercise shows that this inertial behavior of the interest rate is internalized by economic agents through an increase in expected inflation.