Ease of implementation and computational efficiency are two necessary criteria if a simulation system is to be run repeatedly. Described in this paper is a cohort simulation model, based on the theory of terminating renewal processes, which satisfies these two criteria. There are two versions of the model. In one version, waiting times till pregnancy and times spent in the postpartum sterile state, as well as parity progression ratios reflecting hypothetical birth intentions, are taken into account. Unlike simulation systems described in earlier papers, pregnancy wastage is not accommodated in this version of the model. A second version is a model of birth intervals in which parity progression ratios and distributions of waiting times among live births, both of which may reflect pregnancy wastage when based on birth history data, serve as computer input. Female mortality, expressed as a survival function, and a distribution of age at marriage in a cohort are essential parts of both versions of the system. High efficiency in computing the many required convolutions has been obtained by use of a fast Fourier transform algorithm. After an overview of computer software design is given, the computer input for twelve simulation runs is described. These twelve runs are designed to test the impact of various combinations of levels of mortality, age of marriage, and fertility on population growth. One of the interesting substantive conclusions stemming from the simulation runs was that in populations of low mortality and fertility, late age at marriage, as observed in some historical populations, can be a significant factor in increasing the population doubling time.