Annuities: What You Are Actually Buying

The single idea: a present value over a term you do not know

A fixed-term annuity is easy to price: discount n known payments and add them up. A lifetime annuity has no n. What replaces it is a probability. The actuarial present value of a lifetime income of C per year, payable in arrears from age x, is the sum over every future year t of C × (the probability of surviving t years) × (the discount factor for t years). Write it out and it is the ordinary present-value sum from our companion piece with one extra factor inside each term. That one factor is the whole subject: it is what makes the price finite even though the term is unbounded, and it is what the insurer, not you, is being paid to carry.

The figures in this article use a stated, simple and deliberately transparent mortality assumption so that you can reproduce every number: a Gompertz law in which the force of mortality at age a is (1 ÷ 10) × e^((a − 90) ÷ 10). That gives a life expectancy of 21.75 years at 65, a 13.15 percent chance of dying within ten years, and a 20.87 percent chance of reaching 95. It is a plausible illustration, not a real insurer's table — real pricing uses a table specific to the annuitant population, which is longer-lived than the general one because people who buy lifetime income tend to expect to need it. Interest is 4 percent and payments are annual, in arrears. Change any of those inputs and every number below moves.

Summing it, term by term

The table above does the arithmetic for a $10,000-a-year income bought at 65. Year one is worth $10,000 × 0.9914 × 0.9615 = $9,533. Year ten is worth $10,000 × 0.8685 × 0.6756 = $5,867 — the survival factor and the discount factor are each eating into it. Year thirty, at age 95, is worth $644: still a real payment, but 20.87 percent likely and discounted by a factor of 3.24. Add every year and the total is $133,470. Invert it and $100,000 buys $10,000 × ($100,000 ÷ $133,470) = $7,492 a year, a payout rate of 7.49 percent.

Two features of that sum are worth noticing, because they are counter-intuitive in opposite directions. The first twenty years account for $116,858 of the $133,470 — 87.6 percent of the price. Everything from age 95 onward accounts for $2,066, or 1.5 percent. So the deep-old-age tail, the part that frightens people, is almost free in present-value terms. And yet it is precisely that cheap tail that a self-managed portfolio cannot handle, because you cannot spend an expected value: you either reach 100 or you do not, and if you do, a plan built around a life expectancy of 21.75 years has been empty for years. That mismatch — cheap to insure, ruinous to self-insure — is the economic reason lifetime income exists at all.

Why the payout rate beats any safe withdrawal rate — and what part is really the mortality credit

A 7.49 percent payout next to a withdrawal rule of around 4 percent looks like a free lunch, and it is routinely presented as though the mortality credit explained the whole gap. It does not, and the decomposition matters. Take the same 4 percent return and price three different things. Living on interest alone and leaving the capital untouched supports 4.00 percent. Deliberately spending the capital down to zero over a fixed thirty years, to age 95, supports 5.78 percent — that step, 1.78 points, is nothing but return of capital, and any fixed-term plan gets it without an insurer. The lifetime annuity supports 7.49 percent. The remaining 1.71 points is the mortality credit.

So the mortality credit at 65 is real but modest — roughly a fifth of the headline payout, and less than the return-of-capital step it is usually confused with. It is also the only piece of the three that cannot be replicated. Interest you can earn yourself; spending your own capital you can do yourself; but you cannot receive the assets of strangers who died, and you cannot safely plan to run out at a date you do not know. That is what the pool provides: the insurer pays survivors out of a fund that keeps the balances of those who died, so the surviving group earns more than the fund does, and nobody has to guess their own date.

The mortality credit, quantified — small at 65, large at 85

The cleanest way to see the credit as a rate is to ask what extra return a survivor earns in a single year from the pool. If the one-year probability of death is q, the survivors share out the balances of the deceased, so each survivor's account grows by an extra factor of roughly q ÷ (1 − q). Under our assumption q is 0.0086 at 65, which is an extra 0.87 percent a year: a real advantage, but not a dramatic one. At 75 it is 2.37 percent, at 80 it is 3.94 percent, and at 85 it is 6.59 percent — by then the mortality credit alone exceeds any plausible investment return.

That steepness is the practical takeaway, and it explains why payout rates climb so fast with age: 6.67 percent at 60, 7.49 percent at 65, 8.64 percent at 70, 10.27 percent at 75, 12.66 percent at 80. Two forces push in the same direction — a shorter expected term and a larger mortality credit — so the same lump sum buys a much larger income later. Against that, buying later means funding the intervening years yourself, out of the very capital you would otherwise have converted, and bearing the risk that interest rates fall in the meantime. There is no general answer to the timing question; there is only the arithmetic run on your own age, your own capital and the rate available on the day.

The honest costs, one: irreversibility and the rate you lock in

An immediate annuity is normally irreversible. Once the premium is paid the capital is gone: there is nothing to withdraw for a roof, a care home or an emergency, and in most designs nothing to leave. That is not a defect — it is the price of the mortality credit, which only exists because the pool keeps what the deceased did not take. But it means the decision should never involve capital you might need as capital, and it argues for annuitising a part of a portfolio rather than all of it.

The interest rate is locked in the same way, on the day of purchase, for the rest of your life. Under our assumptions a 65-year-old gets 6.03 percent if the pricing rate is 2 percent, 6.75 percent at 3 percent, 7.49 percent at 4 percent and 8.27 percent at 5 percent — a three-point swing in rates moves the income by more than a third. Buying at a moment of low long-term rates therefore fixes a low income permanently, and there is no rebalancing out of it later. Splitting a purchase across several dates is the usual defence, and it costs nothing except the delay.

The honest costs, two: inflation eats a level payment

A level annuity pays the same nominal amount for life, and life is long. At 2.5 percent inflation, purchasing power falls to 78.1 percent after ten years, 61.0 percent after twenty and 47.7 percent after thirty. In money: a $10,000 payment is worth $7,812 after ten years, $6,103 after twenty and $4,767 after thirty. At 2 percent inflation the twenty-year figure is $6,730; at 3 percent it is $5,537. That erosion happens quietly, at exactly the ages when medical and care costs tend to rise, which is the worst possible pairing.

The remedy is an escalating annuity, and its cost is visible immediately. Repricing the same $100,000 at 65 with payments rising 3 percent a year gives a starting income of $5,494 instead of $7,492 — 27 percent less on day one. The escalating payment overtakes the level one in year 12 and is larger thereafter, so the trade is real income now against real income later, decided almost entirely by how long you live. Where an inflation-linked version is offered, read carefully what index it follows and whether the increase is capped, because a capped escalation stops protecting you exactly when protection matters.

The honest costs, three: certainty is bought by lowering the payment

Every feature that reduces the chance of a bad outcome makes the contract cost more to insure, so the payment falls. A joint last-survivor annuity on two 65-year-olds, paying until the second death, prices at 6.32 percent under our assumptions instead of 7.49 — a 15.6 percent smaller payment for a term that is expected to be considerably longer. A ten-year guaranteed period, which pays to your estate if you die early, costs much less: 7.23 percent, only 3.4 percent below the plain version, because the probability of dying within ten years at 65 is just 13.15 percent. That asymmetry is useful to know — a guarantee period is cheap reassurance, joint cover is a substantive change of contract.

The last cost is the one no formula prices: the insurer has to still be there in year thirty. An annuity is an unsecured long-dated promise, so the counterparty matters as much as the payout rate, and a slightly higher payment from a weaker balance sheet is not obviously a better deal. Protection arrangements differ enormously — some countries operate a statutory guarantee scheme for insurance contracts with a defined ceiling, some rely on portfolio-transfer powers instead, and the coverage that applies depends on where the contract is written, not where you live. Ask what supervisory regime the contract falls under and what happens on insolvency, and split large amounts across providers if the answer leaves you uncomfortable.

Frequently asked questions

What happens to my money if I die in the second year?

On a plain single-life annuity, the payments stop and the remaining capital stays with the pool — it is what funds the mortality credit paid to everyone still alive. That is the bargain, stated plainly: you are insuring against living too long, and the premium for that insurance is what happens if you do not. If leaving something matters to you, a guaranteed period or a value-protected option changes it, and the price is visible: under our assumptions a ten-year guarantee costs 3.4 percent of the payment, while a joint annuity covering a second life costs 15.6 percent. Decide which risk you actually want to insure before comparing quotes, because the products are not interchangeable.

Are the figures in this article a quote?

No, and they should not be read as one. Every figure here comes from a transparent illustrative mortality law and a 4 percent interest assumption, chosen so the arithmetic can be reproduced rather than because they match any provider's pricing. A real quote reflects the insurer's own annuitant table, its investment portfolio, its expense and capital charges, your age to the month, sometimes your health and smoking status, and the market on the day. Enhanced terms for a diagnosed condition can differ from standard terms substantially. Use the calculation to understand what drives the price and what questions to ask; get the number itself from providers, in writing, on the same specification.

Is it better to wait and buy at 75 instead of 65?

The payout rate is much higher later — 10.27 percent at 75 against 7.49 percent at 65 under our assumptions — but that is not the same as being better off. Waiting means funding ten years of income from the capital you were going to convert, so there is less capital to convert when you arrive, and you carry the investment and interest-rate risk of that decade yourself. Waiting also means going ten years without the mortality credit, which is the one thing you cannot manufacture. The genuine arguments for waiting are flexibility and the possibility of qualifying for enhanced terms on health grounds; the genuine argument against is that the risk you are insuring is present the whole time. Run both paths with your own numbers rather than choosing on the headline rate.

Why is my expected total of payments larger than what I paid?

Because the two numbers live at different dates. On our assumptions a 65-year-old expects 21.75 years of $10,000, which is $217,500 of nominal payments for a price of $133,470. That is not a profit: money arriving in year twenty is worth 0.4564 of money today at 4 percent, so discounting the whole stream is exactly what brings $217,500 down to $133,470. Comparing a lifetime of undiscounted receipts to a single payment made today is the same error as comparing thirty years of loan instalments to the amount borrowed. If you want a fair comparison, discount both sides, or ask instead how many years it takes to get your capital back in nominal terms — here 13.3 years — and treat that as a break-even, not a return.

Should I annuitise everything?

Nothing in this article can answer that for you, and anyone who answers it without knowing your other income, your health, your obligations and your country's rules is guessing. What the arithmetic does say is structural. An annuity is the only instrument that removes the risk of outliving your capital, and it is uniquely good at that because of the mortality credit; it is also irreversible, exposed to inflation on a level payment, and dependent on one counterparty. Those properties argue for covering essential, non-negotiable spending with guaranteed income — from state pensions, defined-benefit schemes and possibly an annuity — while keeping liquid capital for everything that is discretionary or unpredictable. That is a structure, not a recommendation, and the decision itself needs regulated advice.