Endowment Insurance: Pure and Modified for Actuaries

Pure Endowment

A pure endowment pays a benefit of 1 only if the insured survives to the end of n years. The APV is n_E_x = v^n * n_p_x. This represents the present value of a certain payment discounted for both interest and mortality. Pure endowments are building blocks for annuities: a life annuity-due is the sum of pure endowments a-ddot_x = sum from k=0 to infinity of k_E_x. Pure endowments are also used in pension calculations for projected benefit obligations.

Endowment Insurance

An n-year endowment insurance pays 1 upon death within n years or upon survival to n years, whichever comes first. The APV is A_{x:n} = A_{x:n}^1 + n_E_x (term insurance plus pure endowment). Since the benefit is always paid, the APV is higher than either component alone. The net premium P_{x:n} = A_{x:n} / a-ddot_{x:n} is correspondingly higher. Reserves build substantially over the policy term, reaching the face amount at maturity. Exam LTAM tests endowment insurance extensively in premium and reserve calculations.