As many developed countries face the challenges of an aging population, the need to efficiently plan and finance long-term care (LTC) becomes increasingly important. Understanding the dynamics of care requirements and their associated costs is essential for sustainable healthcare systems. In this study, we employ a multi-state Markov model to analyze the transitions between care states of elderly individuals within institutional LTC in the canton of Geneva, Switzerland. Utilizing a comprehensive dataset of 21 494 elderly residents, we grouped care levels into four broader categories reflecting the range from quasi-autonomy to severe dependency. Our model considers fixed covariates at admission, such as demographic details, medical diagnoses, and levels of dependence, to forecast transitions and associated costs. The main results illustrate significant variations in care trajectories and LTC costs across different health profiles, notably influenced by gender and initial care state. Females generally require longer periods with less intensive care, while conditions like severe and nervous diseases show quicker progression to more intensive care and higher initial costs. These transitions and expected length of stay in each state directly impact LTC costs, highlighting the necessity of advanced strategies to manage the financial burden. Our findings offer insights that can be utilized to optimize LTC services in response to the specific needs of institutionalized elderly people. These findings can be applied to enhance healthcare planning, the preparedness of infrastructure, and the design of insurance products.