Actuarial Present Value Analysis of The Due Temporary Annuity

Abstract

An n-year term life annuity is a number of interest-bearing payments paid by the policyholder during his/her life until death starting from the time of the contract agreement up to n years. In discrete life annuities, the policyholder can make a series of payments at the beginning of the period (due annuity) or the end of the period (immediate annuity). The researcher will analyze the value of the n-year term life annuity paid by the policyholder at the beginning of the payment period using the survival function approach on the Gompertz distribution. The value of the n-year term life annuity is influenced by the magnitude of the discount factor and the survival function on the Gompertz distribution. The researcher will set the age limit of the policyholder starting from 20 years to 40 years with an n-year contract agreement. Using the Maximum Likelihood Method (MLE), the researcher obtains the estimated values ​​of the parameters B and c , respectively, 10^-6 <= B <= 10^-4 and 1,10 <= c <= 1,15. Also, the researcher used interest rates that correspond to BI interest rates (period January 2023 to April 2024) of 5.75%, 6%, and 6.25%. The calculation results show that the higher the interest rate applied, the smaller the actuarial present value for a person aged (x) for a term of n years.