We estimate and trace a credit demand curve for households that recently experienced damage to their homes from a natural disaster. Our administrative data include over one million applicants to a federal recovery loan program for households. We estimate extensive‐margin demand over a large range of interest rates. Our identification strategy exploits 24 natural experiments, leveraging exogenous, time‐based variation in the program's offered interest rate. Interest rates meaningfully affect consumer demand throughout the distribution of rates. On average, a 1 percentage point increase in the interest rate reduces loan take‐up by 26%. We find a large impact of applicants' credit quality on demand and evidence of monthly payment targeting. Using our estimated demand curve and information on program costs, we find that the program generates an average social surplus of $2900 per borrower.