This paper develops a monetary endogenous growth overlapping generations model characterized by endogenous longevity and an inflation targeting monetary authority, and analyzes the growth dynamics that emerges from this framework. Besides the endogenous longevity which depends on the complimentarity of private and public health expenditures, the growth process is endogenized by allowing for a productive role of government expenditure on infrastructure. Following the huge existing literature, money is introduced by assuming that banks are obligated to hold a fraction of the deposits as cash reserve requirements. Given this framework, we show that multiple equilibrium emerges, with the low-growth (high-growth) equilibrium being unstable (stable) and locally determinate (locally indeterminate). In addition, we show that, under certain conditions, endogenous fluctuations and even chaos could emerge around the high-growth equilibrium.