The price elasticity of demand for credit has major implications for macroeconomics, finance, and development. We present estimates of this parameter derived from a randomized trial. The experiment was implemented by a consumer microfinance lender in South Africa and identifies demand curves that, while downward-sloping with respect to price, are flatter than recent estimates in both developing and developed countries throughout most of a wide price range. However, demand becomes highly price sensitive at higher-than-normal rates. We discuss several interpretations of this kink and present some related evidence. We also find that loan size is far more responsive to changes in loan maturity than to changes in interest rate. This pattern is more pronounced among lower income individuals, a comparative static that has been observed in the United States as well and is consistent with liquidity constraints that decrease with income.