Achieving and maintaining zero population growth
In a growing population, it would, in theory, be possible for population growth to stop immediately if fertility rates fell to such low values that the birth rate offset the death rate exactly. However, it would be very difficult to achieve and sustain zero growth in this way, as fertility changes would have to track changes in the CDR caused by changes in the age structure: every time the CDR rose because more people moved into older and high mortality age groups, fertility rates would have to rise to offset this. Every time CDR fell because the older age groups died off and became proportionately less important, fertility rates would have to fall again to compensate for this. It is worth noting that the turbulence in the age structure and crude rates would persist for much longer in the zero growth scenario than the fluctuations due to momentum discussed so far.
In addition to being highly unlikely, the zero population growth scenario is also undesirable. During periods of below replacement fertility, for example, a population ages very fast, and this could cause severe problems if social security and retirement benefits are paid directly from the current workers' contributions (i.e., a pay-as-you-go system of financing social security)