The current state-of-the art motion planners for mobile robots typically do not consider the future movement of moving obstacles. Instead they work by rapid replanning, which makes them reactively adapt to any changes in the environment. This can result in a sub-optimal behavior, which we address in this work by proposing a predictive motion planner that integrates motion predictions into all planning steps. We demonstrate the validity of our approach by evaluating our proposed planner in a dynamic environment where the robot moves slower than the moving obstacles. We benchmark our predictive planner with a reactive planning approach and observe better performance, both in avoiding collisions and maintaining the robots position in the goal region.