Conducting temporal analysis of census data often requires applying areal interpolation to integrate data that have been spatially aggregated using incompatible zoning systems. This article introduces a method of areal interpolation, target-density weighting (TDW), that is useful for long-term temporal analysis because it requires only readily available historical data and basic geographic information system operations. Then, through regression analysis of a large sample of U.S. census tract data, a model is produced that relates the error in TDW estimates of tract population to four basic properties of tracts. An analysis of model residuals combined with theorized absolute limits on interpolation error yields formulas with which we can compute upper and lower prediction bounds on the population in a tract of one census at the time of a different census. These prediction intervals enable the interpretation of different interpolated estimates with appropriately varying degrees of uncertainty.