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This paper develops a finite-lifetime continuous-time model of human capital acquisition. Exogenous technological progress has two aspects, a knowledge frontier and an ease-of-learning parameter. We find that as lifespan increases: (1) output per person-hour rises in a concave fashion, and (2) learning during the work-phase of life only occurs when individuals have a sufficiently long lifespan. As a result, countries that differ in the average lifespan of their inhabitants can have permanently different levels of output per person even in the presence of free trade, perfect capital markets and common production functions. (JEL O33, J24, F43, D91)