Federated learning (FL) is a privacy-preserving learning technique that enables distributed computing devices to train shared learning models across data silos collaboratively. Existing FL works mostly focus on designing advanced FL algorithms to improve the model performance. However, the economic considerations of the clients, such as fairness and incentive, are yet to be fully explored. Without such considerations, self-motivated clients may lose interest and leave the federation. To address this problem, we designed a novel incentive mechanism that involves a client selection process to remove low-quality clients and a money transfer process to ensure a fair reward distribution. Our experimental results strongly demonstrate that the proposed incentive mechanism can effectively improve the duration and fairness of the federation.