We present an exact forward-in-time algorithm that can efficiently simulate the evolution of a finite population under the Wright-Fisher model. We used simulations based on this algorithm to verify the accuracy of the ancestral recombination graph approximation by comparing it to the exact Wright-Fisher scenario. We find that the recombination graph is generally a very good approximation for models with complete outcrossing, whereas, for models with self-fertilization, the approximation becomes slightly inexact for some combinations of selfing and recombination parameters.