The effect of a temporally correlated afferent current on the firing rate of a leaky integrate-and-fire neuron is studied. This current is characterized in terms of rates, autocorrelations, and cross correlations, and correlation time scale tau(c) of excitatory and inhibitory inputs. The output rate nu(out) is calculated in the Fokker-Planck formalism in the limit of both small and large tau(c) compared to the membrane time constant tau of the neuron. By simulations we check the analytical results, provide an interpolation valid for all tau(c), and study the neuron's response to rapid changes in the correlation magnitude.