Increasing life expectancy in modern society is undoubtedly due to improved healthcare, scientific advances in medicine, and the overall healthy lifestyle of the general population. However, this positive trend has led to an increase in the number of older people with a growing need for a sustainable system for the long-term care of this part of the population, which includes social and health services that are essential for a high quality of life. Longevity also brings challenges in the form of a polymorbid geriatric population that places financial pressure on healthcare systems. Regardless, one disease dominates the debate about financial sustainability due to the increasing numbers of people diagnosed, and that is Alzheimer’s disease (AD). The presented paper aims to demonstrate the economic burden of social and healthcare services. Data from two regions in the Czech Republic were selected to demonstrate the potential scope of the problem. The future costs connected with AD are calculated by a prediction model, which is based on a population model for predicting the number of people with AD between 2020 and 2070. Based on the presented data from the two regions in the Czech Republic and the prediction model, several trends emerged. There appears to be a significant difference in the annual direct costs per person diagnosed with AD depending on the region in which they reside. This may lead to a significant inequality of the services a person can acquire followed by subsequent social issues that can manifest as a lower quality of life. Furthermore, given the prediction of the growing AD population, the costs expressed in constant prices based on the year 2020 will increase almost threefold during the period 2020–2070. The predicted threefold increase will place additional financial pressure on all stakeholders responsible for social and healthcare services, as the current situation is already challenging.