The Ramsey-Cass-Koopmans (RCK) model is the cornerstone of most contemporary macroeconomic growth models. Here, the economy is modelled with one representative firm, which utilizes capital and labor for production and one representative household, which receives compensation for providing these factors. While this basic model and its numerous extensions are based in microeconomic decision making, they still remain deterministic representative agent models. This limits the realism severely and precludes any non-equilibrium dynamics and emergent phenomena such as bubbles and crashes. Given the empirical evidence such as the financial crisis in 2008, it is vital to upgrade this model with modern complexity economics approaches such as agent-based modelling. In this work, we develop an agent-based RCK model which can generate rich dynamics such as highly skewed wealth distributions whilst maintain- ing an economically optimal effective savings rate. This reveals that households that set their own savings rate using a myopic ‘imitate-the-best’ heuristic can act, on aggregate, similar to the omniscient, optimizing representative agent. However, we find this optimality is achieved only for certain rates of social interaction, for which the agents partition themselves into a high- and a low-savings rate group with corresponding levels of capital. For higher rates of social interaction, we find myopic behavior leading to smaller unimodal savings rates, thus providing a clear relationship between the time-scale of social learning and the discount rate in the standard RCK model. Furthermore, for fairly realistic parameter estimates, we find the 30-year capital autocorrelations in the bimodal savings rate regime to be in line with empirical findings of intergenerational wealth correlations. With this work, we provide a more complex and potent model which shows realistic dynamics and can form the basis for a new class of agent-based macroeconomic models.