Vehicle third-party liability insurance, or civil liability insurance, is not only the most important but above all mandatory insurance for every vehicle owner. Third-party liability insurance covers the costs of repairing damage caused by the insured to other road users. Therefore, vehicle third-party liability insurance protects not so much the insured themselves, but rather third parties who receive financial compensation for damages incurred and compensation for bodily injury. This study analyzed the relationships between vehicle insurance policyholders and individuals involved in road accidents. To achieve this, the age structure of individuals purchasing private car policies and the age structure of individuals involved in road accidents were analyzed. Insurance companies calculate the premium amount taking into account many factors related to both the driver and the vehicle. The age of the owner, years of driving experience, claims history, place of residence, and marital status are important factors. The age and brand of the car, as well as the engine capacity, are also significant. The study also presents the average amounts of vehicle third-party liability insurance in selected European countries along with the number of road accidents. The results confirm that accidents caused by young drivers are more tragic in their consequences, so young and inexperienced drivers must expect significantly higher costs when purchasing mandatory third-party liability insurance.