Video Moment Retrieval (VMR) aims at retrieving the most relevant events from an untrimmed video with natural language queries. Existing VMR methods suffer from two defects: (1) massive expensive temporal annotations are required to obtain satisfying performance; (2) complicated cross-modal interaction modules are deployed, which lead to high computational cost and low efficiency for the retrieval process. To address these issues, we propose a novel method termed Cheaper and Faster Moment Retrieval (CFMR), which well balances the retrieval accuracy, efficiency, and annotation cost for VMR. Specifically, our proposed CFMR method learns from point-level supervision where each annotation is a single frame randomly located within the target moment. It is 6 times cheaper than the conventional annotations of event boundaries. Furthermore, we also design a concept-based multimodal alignment mechanism to bypass the usage of cross-modal interaction modules during the inference process, remarkably improving retrieval efficiency. The experimental results on three widely used VMR benchmarks demonstrate the proposed CFMR method establishes new state-of-the-art with point-level supervision. Moreover, it significantly accelerates the retrieval speed with more than 100 times FLOPs compared to existing approaches with point-level supervision.