This article gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model. In an economy where high (low) growth rates of population lead to a growth path that is efficient (inefficient), there always exists an interior optimum growth rate for population. In all other cases, there exists no interior optimum. The Serendipity Theorem, however, does, in general, not hold in an economy with government debt. Moreover, the growth rate for population that leads an economy with debt to a golden rule allocation can never be optimal.