  An important question in economics is how people choose between different
payments in the future. The classical normative model predicts that a decision
maker discounts a later payment relative to an earlier one by an exponential
function of the time between them. Descriptive models use non-exponential
functions to fit observed behavioral phenomena, such as preference reversal.
Here we propose a model of discounting, consistent with standard axioms of
choice, in which decision makers maximize the growth rate of their wealth. Four
specifications of the model produce four forms of discounting -- no
discounting, exponential, hyperbolic, and a hybrid of exponential and
hyperbolic -- two of which predict preference reversal. Our model requires no
assumption of behavioral bias or payment risk.
