Demographic aging results in a growing number of older people in need of care in many regions all over the world. Germany has witnessed steady population aging for decades, prompting policymakers and other stakeholders to discuss how to fulfill the rapidly growing demand for care workers and finance the rising costs of long-term care. Informed decisions on this matter to ensure the sustainability of the statutory long-term care insurance system require reliable knowledge of the associated future costs. These need to be simulated based on well-designed forecast models that holistically include the complexity of the forecast problem, namely the demographic transition, epidemiological trends, concrete demand for and supply of specific care services, and the respective costs. Care risks heavily depend on demographics, both in absolute terms and according to severity. The number of persons in need of care, disaggregated by severity of disability, in turn, is the main driver of the remuneration that is paid by long-term care insurance. Therefore, detailed forecasts of the population and care rates are important ingredients for forecasts of long-term care insurance expenditures. We present a novel approach based on a stochastic demographic cohort-component approach that includes trends in age- and sex-specific care rates and the demand for specific care services, given changing preferences over the life course. The model is executed for Germany until the year 2050 as a case study.