Public debt can be optimal in standard incomplete market models with infinitely lived agents, since the associated capital crowd-out induces a higher interest rate. The higher interest rate encourages individuals to save and, hence, better self-insure against idiosyncratic labor earnings risk. Even though individual savings behavior is a crucial determinant of the optimality of public debt, this class of economies abstracts from empirically observed life cycle savings patterns. Thus, this paper studies how incorporating a life cycle affects optimal public debt. We find that while the infinitely lived agent model's optimal policy is public debt equal to 24\% of output, the life cycle model's optimal policy is public savings equal to 61\% of output. Although public debt also encourages life cycle agents to hold more savings during their lifetimes, the act of accumulating this savings mitigates the potential welfare benefit. Moreover, public savings improves life cycle agents' welfare by encouraging a flatter allocation of consumption and leisure over their lifetimes. Accordingly, abstracting from the life cycle yields an optimal policy that reduces average welfare by more than 0.6% of expected lifetime consumption. Furthermore, ignoring the life cycle overstates the influence of wealth inequality on optimal policy, since optimal policy is far less sensitive to wealth inequality in the life cycle model than in the infinitely lived agent model. These results demonstrate that studying optimal debt policy in an infinitely lived agent model, which abstracts from the realism of a life cycle in order to render models more computationally tractable, is not without loss of generality.