This paper studies the effects of uncertain lifetime on capital accumulation and growth and also the sensitivity of those effects to the existence of a perfect annuities market. The model is an overlapping generations model with uncertain lifetimes. The technology is convex and such that the marginal product of capital is bounded away from zero. A contribution of this paper is to show that the existence of accidental bequests may lead the economy to an equilibrium that exhibits asymptotic growth, which is impossible in an economy with a perfect annuities market or with certain lifetimes. This paper also shows that if individuals face a positive probability of surviving in every period, they may be willing to save at any age. This effect of uncertain lifetime on savings may also lead the economy to an equilibrium exhibiting asymptotic growth even if there exists a perfect annuities market.