Smart Grid (SG) is a next-generation electrical power system that use two way communication in the generation, consumption and delivery of the electrical energy. One of the key feature of SG is Demand Response (DR). In DR a pricing signal is provided to the customer via smart meters, and customer modifies their demand in response to price signals. However, most of the load scheduling schemes used day-ahead or Time of Use pricing scheme, these schemes are deviating from Real-time Pricing (RTP) scheme. In this paper, an RTP based scheduling scheme is proposed using Optimal Stopping Rule (OSR). An OSR gives the best operating time of the device to reduce electricity bills. The cost minimization problem is formulated as an unconstrained optimization problem. Moreover, waiting time cost is also formulated as sub problem to reduce waiting time of the device. Waiting time is considered as a function of cost. After that, an algorithm is proposed to solve this optimization problem for various types of loads. Simulation results verify that proposed algorithm has low computational complexity and reduce electricity bill with less waiting time.