In this paper, we develop an optimal EOQ inventory model for deteriorating items considering constant demand, inflation factor and time dependent deterioration rate over a finite time horizon. Shortages are allowed and excess demand is backlogged. The aim of this model is to determine the optimal decision variables so that the net present value of total system cost over a finite planning horizon is minimized and the profit function is maximized. For the general model, we give the equations for the optimal policy and cost function. Further, the necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. A numerical example is given to illustrate the solution procedure of the model. Finally, based on this example, we conduct a sensitivity analysis of the model.