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Bonus-malus system determines the premium value based on the claim history of each policyholder. The bonus is a decrease in premium value in the next period for policyholders who do not submit claims in the previous period. Conversely, malus is an increase in premium value for policyholders who submit claims. This article discusses the classic and optimal bonus-malus systems in vehicle insurance. The classic bonus-malus system sets premium value based on the frequency of claims, while the optimal bonus-malus system sets premium values based on both frequency and severity of claims. In premium calculation, the Bayes method was used which can describe the expectation value of a datum within a period based on historical data. The results obtained in this paper are classic and optimal bonus-malus premium tables. The tables are, essentially, in a form of a product which can be offered to prospective customers by insurance companies.