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In different areas of research, multiple recurrent competing risks (RCR) are often observed on the same observational unit. For instance, different types of cancer relapses are observed on the same patient and several types of component failures are observed in the same reliability system. When a terminal event (TE) such as death is also observed on the same unit, since the RCRs are generally informative about death, we develop joint dynamic models that simultaneously model the RCRs and the TE. A key interest of such joint dynamic modeling is to predict time-to-terminal event (TTTE) for new units that have not experienced the TE by the end of monitoring period. In this paper, we propose a simulation approach to predict TTTE which arises from a class of joint dynamic models of RCRs and TE. The proposed approach can be applied to problems in precision medicine and potentially many other settings. The simulation method makes personalized predictions of TTTE and provides an empirical predictive distribution of TTTE. Predictions of the RCR occurrences beyond a possibly random monitoring time and leading up to the TE occurrence are also produced. The approach is dynamic in that each simulated occurrence of RCR increases the amount of knowledge we obtain on an observational unit which informs the simulation of TTTE. We demonstrate the approach on a synthetic dataset and evaluate predictive accuracy of the prediction method through 5-fold cross-validation using empirical Brier score.