This paper explores differentially-private federated learning (FL) across time-varying databases, delving into a nuanced three-way tradeoff involving age, accuracy, and differential privacy (DP). Emphasizing the potential advantages of scheduling, we propose an optimization problem aimed at meeting DP requirements while minimizing the loss gap between the aggregated model and the model obtained without DP constraints. To harness the benefits of scheduling, we introduce an age-dependent upper bound on the loss, leading to the development of an age-aware scheduling design. Simulation results underscore the superior performance of our proposed scheme compared to FL with classic DP, which does not consider scheduling as a design factor. This research contributes insights into the interplay of age, accuracy, and DP in FL, with practical implications for scheduling strategies.