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We study the problem of scheduling periodic real-time tasks which have individual minimum reward requirements. We consider situations where tasks generate jobs that can be provided arbitrary service times before their deadlines, and obtain rewards based on the service times received by the jobs of the task. We show that this model is compatible with the imprecise computation models and the increasing reward with increasing service models. In contrast to previous work on these models, which mainly focus on maximizing the total reward in the system, we additionally aim to fulfill different reward requirements by different tasks. This provides better fairness and also allows fine-grained tradeoff between tasks. We first derive a necessary and sufficient condition for a system with reward requirements of tasks to be feasible. We next obtain an off-line feasibility optimal scheduling policy. We then study a sufficient condition for a policy to be feasibility optimal or achieve some approximation bound. This condition serves as a guideline for designing on-line scheduling policy and we obtain a greedy policy based on it. We prove that the on-line policy is feasibility optimal when all tasks have the same periods, and also obtain an approximation bound for the policy under general cases. We test our policies in comparative simulations.