The topic of the thesis is Life Insurance and clarification of the three basic types of life insurance: Pure Endowment, Risk Insurance and Endowment. In the first chapter of the paper, we described the basic concepts of financial mathematics for easier monitoring of the paper below. In the second chapter, we got introduced with a mortality table that contains one of the most important demographic indicators - the probability of death, which is used to obtain other indicators such as life expectancy, which is an important factor for calculating the amount of the premium in the life insurance segment. We begin with the elaboration of the topic in the third chapter, where we introduce some basic definitions of life insurance, types and examples of the most represented insurance on the market, which is endowment that covers both risks, the one for death and for survival. Premium is the price you pay for the policy, and we distinguish two types of premium: net premium and gross premium. In the last chapter we presented the formulas for their calculation, where we showed the theoretical calculation of premiums and the components that affect the calculation. With the example of a policy from real life, we have shown that the gender, state of health, and profession play an important role in determining the amount of the premium, which we did not take into account during the theoretical calculation.