End users equipped with storage may exploit time variations in electricity prices to earn profit by doing energy arbitrage, i.e., buying energy when it is cheap and selling it when it is expensive. We propose an algorithm to find an optimal solution of the energy arbitrage problem under given time varying electricity prices. Our algorithm is based on discretization of optimal Lagrange multipliers of a convex problem and has a structure in which the optimal control decisions are independent of past or future prices beyond a certain time horizon. The proposed algorithm has a run time complexity of O(N 2) in the worst case, where N denotes the time horizon. To show the efficacy of the proposed algorithm, we compare its run-time performance with other algorithms used in MATLAB's constrained optimization solvers. Our algorithm is found to be at least ten times faster, and hence has the potential to be used for in real-time. Using the proposed algorithm, we also evaluate the benefits of doing energy arbitrage over an extended period of time for which price signals are available from some ISO's in USA and Europe.