Entrepreneurs appear to borrow largely against their near-term revenues, even when their investment has a longer horizon. In this paper, we develop a model of credit horizons. A question of particular concern to us is whether persistently low interest rates can stifle economic activity. With this in mind, our model is of a small open economy where the world interest rate is taken to be exogenous. We show that a permanent fall in the interest rate can reduce aggregate investment and growth, and even lead to a drop in the welfare of everyone in the domestic economy. We use our framework to examine how credit horizons interact with plant dynamics and the evolution of productivity. Finally, we speculate that the measurement of total investment may camouflage the true level of productive investment in plant and human capital, and give too rosy a picture of property-fuelled booms sparked by low interest rates.