How does the value of life affect annuity demand? To address this question, we construct a portfolio choice problem with three key features: i) agents have access to life-contingent assets, ii) they always prefer living to dying, iii) agents have non-expected utility preferences. We show that as utility from being alive increases, annuity demand decreases (increases) if agents are more (less) averse to risk rather than to intertemporal fluctuations. Put differently, if people prefer early resolution of uncertainty, they are less interested in annuities when the value of life is high. Our findings have two important implications. First, we get a better understanding of the well-known annuity puzzle. Second, we argue that the observed low annuity demand provides evidence that people prefer early rather than late resolution of uncertainty.