ANNUAL PREMIUM CALCULATION ON SINGLE LIFE INSURANCE USING GOMPERTZ MORTALITY ASSUMPTIONS

Abstract

Premium calculation is one of the important aspects to insurance companies. Careless determination of the premium price can cause the insurance company to fail to bear the risk that the company has. There are several ways to determine premium payments. In this research the premium calculation will be computed using Gompertz mortality assumptions which will be applied to the annual premium calculation of whole life and term life single life insurance of man and woman. The benefit assumed, interest rate, Insurer age, Gompertz parameter and several actuarial notations such as life annuity-due and net single premium is needed in the premium calculation using Gompertz mortality assumptions. This research uses the data of Indonesian Mortality table (TMI IV) and the Linear Least Squares (LLS) method to find the Gompertz parameter to find the survival probabilities. Based on the calculation performed in this research, the value of the premium using Gompertz assumptions is influenced by parameters on the Gompertz assumptions, the interest rate used, and the Insured age. Using the LLS method the parameter found for woman is 0.00006592 for B and 1.083 for c and the parameter for man is 0.00009501 for B and 1.082795 for c. Moreover, the value of the premium based on Gompertz mortality assumptions using Linear Least Squares (LLS) method with the same age of 30 years old for man is higher than the value of the premium for woman, with the value of IDR 6,020,436.98 for man and IDR 4,808,984.04 for woman using whole life insurance and the value of IDR 2,342,104.10 for man and IDR 1,644,897.21 for woman using term life insurance.