actuarial present value (EPV)
/ EE-pee-vee / A-P-V /
Imagine you promise to pay someone $100,000 — but only if they die during the next year, and only if they live to collect a birthday cheque, and the payment lands sometime in the future. Two things make that promise worth less than $100,000 today. First, money in the future is worth less than money now, because money today can earn interest (the time value of money). Second, the payment might never happen at all — it depends on whether a person lives or dies. The actuarial present value is the single fair number that bundles both of these effects together: how much that uncertain, future, life-contingent promise is worth right now.
Mechanically, you take every possible future payment, shrink it for interest back to today (discounting), and then weight each shrunken amount by the probability that it actually gets paid. Add up all those probability-weighted, discounted amounts and you have the actuarial present value — which is why it is also called the expected present value (EPV). A tiny example in words: a benefit of 1 paid at the end of a year only if a person dies during that year is worth, today, the discount factor for one year multiplied by that person's probability of dying within the year. If interest discounts a future 1 down to about 0.95, and the chance of dying is 0.01, the actuarial present value is about 0.95 times 0.01, roughly 0.0095.
This is the foundation stone of all life actuarial work. Premiums, reserves, the price of an annuity, the value of a pension promise — all of them are built by computing actuarial present values of benefits and of payments and then comparing the two. The word 'expected' is important and easy to misread: the EPV is an average over many possible futures, not a prediction of what will happen to any one person. No single policyholder ever 'gets' the EPV; it is the right price across a large pool, where the law of large numbers makes the average reliable.
A pure endowment pays 1 in 5 years only if a person now aged 60 is still alive. If the 5-year discount factor is v^5 = 0.78 and the probability of surviving 5 years is 0.95, the actuarial present value is 0.78 x 0.95 = 0.741.
Discount for interest, then weight by survival — the two effects multiplied.
'Expected' does not mean 'most likely' or 'what will happen' — the EPV is a probability-weighted average across many futures, and almost no individual outcome equals it.