We present a computational model performing the n-back task. This task requires a number of cognitive processes including rapid binding, updating, and retrieval of items in working memory. The model is implemented in spiking leaky-integrate-and-fire neurons with physiologically constrained parameters, and anatomically constrained organization. The methods of the Semantic Pointer Architecture (SPA) are used to construct the model. Accuracies and reaction times produced by the model are shown to match human data. Namely, characteristic decline in accuracy and response speed with increase of n is reproduced. Furthermore, the model provides evidence, contrary to some past proposals, that an active removal process of items in working memory is not necessary for an accurate performance on the n-back task.