Access to financial data is challenging due to privacy and regulatory concerns. This paper introduces MoMTSimDP, a mobile money transaction simulator that integrates differential privacy (DP) into agent-based modeling (ABM) to provide formal privacy guarantees in simulations. MoMTSimDP not only replicates the statistical behaviors of transactional data but also ensures privacy through DP, a rigorous mathematical framework for privacy preservation. We calibrate MoMTSimDP using differentially private statistics derived from real transaction data, including details on client profiles and aggregated transaction metrics such as the count of transactions, total and average transaction amounts, and standard deviations. The validity of the synthetic data produced was assessed using the sum of squared errors method to evaluate its statistical closeness to real data. We report a low total error of 2.0070 between the real and synthetic data. This study demonstrates the application of DP in ABM for simulating financial transactions with formal privacy guarantees.