Pronounced discounting of future rewards has been explained by either preferences or a variety of psychological motives, ranging from self-control issues to difficulties imagining future utilities. Here, I depart from these traditional explanations by modelling reward discounting as noisy numerical perception of described time delays. The model thus resolves a long-standing puzzle in the economics literature—why substantial discounting is routinely observed in experiments using monetary payoffs instead of consumption. The model furthermore predicts different types of non-standard discounting patterns, which are difficult to reconcile under extant discounting models. Two experiments provide support for the stylized behavioural patterns predicted by the model. Denominating equivalent delays in either weeks or days is found to substantially impact behaviour. This finding cannot be organized based on either psychological or preference-based explanations of discounting, but is predicted by the noisy numerical perception framework I present.