The analysis of the determinants of economic growth has allowed the development of extensive literature that has recognized the role of human capital as the main explanatory variable of countries' economic growth. However, the evidence indicates that this relationship does not always occur in a precise way Therefore, it is necessary to analyse the dynamics of each economy. In Colombia, although there is empirical evidence that correlates the variables of economic growth and human capital, there is little research that explains the expected behaviour of growth and human capital in the long term. The objective of this research was to determine the interactions between human capital and economic growth in long-term dynamics in Colombia. For this purpose, a dynamic stochastic general equilibrium (DSGE) model was applied with parameters calibrated from the empirical evidence in Colombia. The results of the DSGE model indicate that economic growth perceives a positive effect in the long term. Disturbances in education productivity captured through the student-professor ratio in tertiary education demonstrate the existence of a causality of this variable towards GDP per capita, and as in the DSGE model, the variables perceive convergences to new equilibria. It is concluded for both models that in the long term, physical capital and human capital have a positive relationship with economic growth.