pure endowment

A pure endowment is the most stripped-down life-contingent promise there is: pay a fixed amount on a future date, but only if the person is still alive then. If they have died before that date, nothing is paid — there is no death benefit and no refund. It is a bet on living, the mirror image of a death benefit. Think of a grandparent setting aside money to give a grandchild on their 21st birthday, on the condition that the grandparent is alive to hand it over.

Its value is wonderfully simple to compute, because the payment is fixed in amount and timing, and only one uncertainty matters — survival to the maturity date. The actuarial present value of an n-year pure endowment of 1 on a life aged x is the n-year discount factor multiplied by the probability that the person survives those n years. In standard notation this is written nE_x = v^n times nP_x, where v^n discounts for interest and nP_x is the survival probability. So if v^5 = 0.78 and the chance of surviving 5 years is 0.95, the pure endowment is worth 0.78 times 0.95 = 0.741 today.

On its own the pure endowment is rarely sold — people dislike the idea of paying in and getting nothing back if they die early. But it is a fundamental building block. An endowment insurance, for example, is exactly a term insurance (pays on death within the period) plus a pure endowment (pays on survival to the end), so that something is paid either way. The pure endowment is also where the survival side of life contingencies enters most cleanly, making it the natural first example when learning the subject.