We study a closed economy featuring heterogeneous agents and exhibiting endogenous economic growth due to interfirm external effects. Individual agents differ in terms of their mortality profile. At birth, nature assigns a health status to each agent. Health type is private information and annuity firms can only observe an agent’s age. In the presence of longevity risk, agents want to annuitize their wealth conform the classic result by Yaari (1965). In the first-best case with perfect annuities, the market would feature a separating equilibrium (SE) in which each health type obtains an actuarially fair perfect insurance. In the SE all agents are savers throughout their lives. The informational asymmetry precludes the attainment of the first-best equilibrium, however, as healthy individuals have a strong incentive to misrepresent their type by claiming to be unhealthy. Using the equilibrium concept of Pauly (1974) and Abel (1986), we prove the existence of a second-best pooling equilibrium (PE) in which individuals of all types annuitize at a common pooling rate. As the unhealthy get close to their maximum attainable age, the pooling rate prompts such individuals to become net borrowers. But borrowing would reveal their health status, so the best the unhealthy can do is to impose a borrowing constraint on themselves during their autumn years. Using a plausibly calibrated version of the model we find that the growth- and welfare effects of PE versus SE are rather small, whilst those of PE versus no annuities at all (NAE) are rather large. An imperfect insurance is better than no insurance at all, both at the microeconomic and at the macroeconomic level.