This paper analyses the theoretical relevance of the dynamical aspects of growth on the discussion about the observed positive correlation between per capita real income and real exchange rates. With this purpose, we develop a simple exogenous growth model where the internal, external and intertemporal equilibrium conditions of a typical macroeconomic model are imposed; this last one through the inclusion of a balanced growth path for the foreign assets accumulation. The main result under this consideration is that the relationship defended by the Balassa-Samuelson hypothesis is no more so straightforward. In our particular approach, the mentioned bilateral relationship depends on a parameter measuring thriftiness in the economy. Therefore, the probability of ending up with a positive relationship between growth and real exchange rates -as the classical economic theory predicts- will be higher when the economy is able to maintain a minimum saving ratio. Moreover, given that our model considers a simple Keynesian consumption function, some explosive paths can also be possible.