Battery energy storage systems (BESSs) have the potential to reduce end users' electricity bills by shifting their grid demand in response to price incentives. Some electricity retailers charge end users for their peak demand in the billing cycle regardless of the time of occurrence. Yet, using BESSs to reduce demand charges is challenging, since the net demand of end users can be highly uncertain due to low aggregation and on-site renewable generation. In this article, an approximate dynamic programming (ADP) methodology is developed to control a BESS to minimize an end user's electricity bill, which includes both an energy charge and monthly peak demand charge. To address time-varying uncertainty, the net demand is modeled using a periodic autoregressive (PAR) model, which is then used to formulate a Markov Decision Process whose objective is to minimize the sum of energy, peak demand, and battery usage costs. A backward ADP strategy is developed which is enabled by new closed-form expressions for the probability distribution of the expected stage and tail costs when a radial basis function (RBF) value function approximation (VFA) is employed. The approach is applied to real net demand data from a small Australian residential community and compared to two benchmark policies: a lookup table VFA and a model predictive control (MPC) approach. The results show that the proposed approach reduces the average monthly peak demand by about 25% (yielding an 8% reduction in the electricity bill), whereas the best-performing benchmark policy reduced the peak demand by about 17%.