Precautionary saving in response to uninsurable income risk can in principle explain the stylized fact that aggregate saving increases with the variance of income, but it is controversial how much of the observed variation in incomes is, in fact, unpredictable. Borrowing constraints offer an alternative explanation that does not require consumers to be uncertain about their future income. This paper employs a three-cohort, overlapping generations model with quadratic utility and no capital to show that, if agents are patient enough, heterogeneity alone can account for more than half the decrease in the equilibrium interest rate caused by a borrowing constraint. The possibility of facing a binding borrowing constraint in the future induces saving, and this saving increases with the cross-sectional variation in income. Another channel that pushes down the interest rate is the direct effect caused by currently constrained agents not being allowed to dissave. For patient agents, the two channels have roughly the same impact on the interest rate.