The demographic change towards a larger proportion of older individuals challenges universal health care systems in sustaining high-quality care and universal coverage without budget expansions. To build valuable predictions of the economic burden from population ageing, it is crucial to understand the determinants of individual-level health care expenditures. Often, the focus has been on the relative importance of an individual’s age and time to death, while only a few newer studies highlight that individual-level health care expenditures are increasing faster for the elderly—i.e., creating a steepening of the individual-level health care expenditure curve over time. Applying individual-level administrative data for the entire Danish population, our study is the first to use a single data set to examine whether age, time to death, and a steepening of the individual-level health care expenditure curve all contributed to individual-level health care expenditures over a 12 year observation period (2006–2018). We find that individual-level expenditures are associated with an individual’s age, an individual’s time to death, and a steepening of the expenditure curve, with the steepening driven by individuals above age 75. We observe heterogeneity in the extent and age distribution of steepening across disease groups. The threefold combination of an ageing population, the correlation between expenditures and age per se, and a steepening of the expenditure curve make establishing financially sustainable universal health care systems increasingly difficult. To mitigate budgetary pressure, policy-makers should stimulate cost-effective medical advances and health care utilization in the treatment of elderly. Moreover, steepening scenarios should be added to future health care expenditure forecasts.