This paper applies the Ramsey–Cass–Koopmans (RCK) growth model to an open economy so that, when calibrated with standard parameter values that are commonly used in the small open economy macroeconomic literature, the time paths of the model variables and the speeds of convergence implied by the model conform with empirical evidence. Open-economy versions of the RCK growth model lead to several counterfactual conclusions including: infinite speeds of convergence for physical capital and output; and unbalanced consumption and asset growth. We avoid these undesired results by extending the baseline model with human capital, international credit constraints, and finite horizons. Given its finite-horizons feature, our model allows us to study the growth implications of changes in life expectancy from the perspective of an open economy, as most of the existing theoretical-quantitative literature that focus on the relationship assumes a closed economy. The model predicts that increased life expectancy has positive but diminishing marginal effect on long-run output per capita. We find that, between 1960 and 2018, improvements in average life expectancy at birth raised long-run output per capita in sub-Saharan Africa, the OECD region, and Canada by an estimated 57.49 %, 14.94 %, and 11.58 %, respectively. In addition, if average life expectancy at birth in sub-Saharan African countries converges from its current level to the level in their OECD counterparts, the region’s long-run output per capita will increase by an estimated 22.89 %.