If the central bank follows an interest rate rule, then inflation is likely to be persistence, even when prices are fully flexible. Any shock, whether persistent or not, may lead to inflation persistence. In equilibrium, the dynamics of inflation are determined by the evolution of the spread between the real interest rate and the central bank's target. Inflation persistence in U.S. data can be characterized by a vector autocorrelation function relating inflation and deviations of output from trend. This paper shows that a flexible-price general equilibrium business cycle model with money and a central bank using an interest rate target can account for such inflation persistence.