We introduce a Monte Carlo algorithm which simulates first-order temperature programmed desorption spectra using the correct connection between Monte Carlo simulation time and real time. The TPD spectra obtained from the Monte Carlo simulations are exactly the same as those calculated from the governing continuum differential equation for a noninteracting system. We discuss in some detail the effects of lateral interactions between adsorbates on the temperature programmed desorption spectra. We find that peak splitting of the temperature programmed desorption spectra characterizes an adsorbate configuration transition on the surface. Furthermore, we analyze in detail the behavior of the coverage-dependent activation energy and preexponential factor for the case of a repulsive nearest-neighbor interaction and find that kinetic compensation occurs in this case.