The payment stream from the issuer to the annuitant has an unknown duration based principally upon the date of death of the annuitant. At this point the contract will terminate and the remainder of the fund accumulated is forfeited unless there are other annuitants or beneficiaries in the contract. Thus a life annuity is a form of longevity insurance, where the uncertainty of an individual's lifespan is transferred from the individual to the insurer, which reduces its own uncertainty by pooling many clients. Annuities can be purchased to provide an income during retirement, or originate from a structured settlement of a personal injury lawsuit.
Ulpian is credited with generating an actuarial life annuity table between AD 211 and 222. Medieval German and Dutch cities and monasteries raised money by the sale of life annuities, and it was recognized that pricing them was difficult. The early practice for selling this instrument did not consider the age of the nominee, thereby raising interesting concerns. These concerns got the attention of several prominent mathematicians over the years, such as Huygens, Bernoulli, de Moivre and others: even Gauss and Laplace had an interest in matters pertaining to this instrument.
It seems that Johan de Witt was the first writer to compute the value of a life annuity as the sum of expected discounted future payments, while Halley used the first mortality table drawn from experience for that calculation. Meanwhile, the Paris Hôtel-Dieu offered some fairly priced annuities that roughly fit the Deparcieux table discounted at 5%.
Continuing practice is an everyday occurrence with well-known theory founded on robust mathematics, as witnessed by the hundreds of millions worldwide who receive regular remuneration via pension or the like. The modern approach to resolving the difficult problems related to a larger scope for this instrument applies many advanced mathematical approaches, such as stochastic methods, game theory, and other tools of financial mathematics.
Annuities that make payments in fixed amounts or in amounts that increase by a fixed percentage are called fixed annuities. Variable annuities, by contrast, pay amounts that vary according to the investment performance of a specified set of investments, typically bond and equity mutual funds.
Variable annuities are used for many different objectives. One common objective is deferral of the recognition of taxable gains. Money deposited in a variable annuity grows on a tax-deferred basis, so that taxes on investment gains are not due until a withdrawal is made. Variable annuities offer a variety of funds from various money managers. This gives investors the ability to move between sub accounts without incurring additional fees or sales charges.
Variable annuities have been criticized for their high commissions, contingent deferred sale charges, tax deferred growth, high taxes on profits, and high annual costs. Sales abuses became so prevalent that in November 2007, the Securities and Exchange Commission approved FINRA Rule 2821 requiring brokers to determine specific suitability criteria when recommending the purchase or exchange (but not the surrender) of deferred variable annuities.
With a "single premium" or "immediate" annuity, the "annuitant" pays for the annuity with a single lump sum. The annuity starts making regular payments to the annuitant within a year. A common use of a single premium annuity is as a destination for roll-over retirement savings upon retirement. In such a case, a retiree withdraws all of the money he/she has saved during working life in, for example, The advantage of such an annuity is that the annuitant has a guaranteed income for life, whereas if the retiree were instead to withdraw money regularly from the retirement account he/she might run out of money before death, or alternatively not have as much to spend while alive as could have been possible with an annuity purchase. Another common use for an income annuity is to pay recurring expenses, such as assisted living expenses, mortgage or insurance premiums.
The disadvantage of such an annuity is that the election is irrevocable and, because of inflation, a guaranteed income for life is not the same thing as guaranteeing a comfortable income for life.