Policymakers often prescribe that microfinance institutions increase interest rates to eliminate their reliance on subsidies. This strategy makes sense if the poor are rate insensitive: then microlenders increase profitability (or achieve sustainability) without reducing the poor's access to credit. We test the assumption of price inelastic demand using randomized trials conducted by a consumer lender in South Africa. The demand curves are downward sloping, and steeper for price increases relative to the lender's standard rates. We also find that loan size is far more responsive to changes in loan maturity than to changes in interest rates, which is consistent with binding liquidity constraints.