In an extremely competitive market such as supplementary health, it is of fundamental importance to build advantages over competing companies. In economies of scale, one way to become competitive is to keep prices in a cluster smaller than the competition. The present study aims to show a simplified procedure for the determination of per capita care costs and also show the importance of the size of the insured group for the technical solvency charge, a direct consequence of the Large Numbers Act, first described by Jakob Bernoulli. For this purpose, historical data were used, using the Monte Carlo simulation technique. The research is classified methodologically as bibliographical, documentary and laboratory in computer environment. The data are real and were obtained from a health care provider in the city of Fortaleza. In practical terms, this study collaborated with decision-makers working in the area of supplementary health, regarding the determination of the cost of care, a component of the price to be charged by a health plan.