A life annuity is an
annuity In investment, an annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account, m ...
, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. The majority of life annuities are
insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to hedge ...
products sold or issued by life insurance companies however substantial case law indicates that annuity products are not necessarily insurance products. Annuities can be purchased to provide an income during retirement, or originate from a ''
structured settlement A structured settlement is a negotiated financial or insurance arrangement through which a claimant agrees to resolve a personal injury tort claim by receiving part or all of a settlement in the form of periodic payments on an agreed schedule, ra ...
'' of a personal injury
lawsuit - A lawsuit is a proceeding by a party or parties against another in the civil court of law. The archaic term "suit in law" is found in only a small number of laws still in effect today. The term "lawsuit" is used in reference to a civil acti ...
. Life annuities may be sold in exchange for the immediate payment of a lump sum (single-payment annuity) or a series of regular payments (flexible payment annuity), prior to the onset of the annuity. 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.


The instrument's evolution has been long and continues as part of actuarial science.
Ulpian Ulpian (; la, Gnaeus Domitius Annius Ulpianus; c. 170223? 228?) was a Roman jurist born in Tyre. He was considered one of the great legal authorities of his time and was one of the five jurists upon whom decisions were to be based according to ...
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.From Commercial Arithmetic to Life Annuities: The Early History of Financial Economics, 1478-1776
" Geoffrey Poitras, Simon Fraser University
These concerns got the attention of several prominent mathematicians over the years, such as Huygens, Bernoulli, de Moivre and others: even
Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
and Laplace had an interest in matters pertaining to this instrument. It seems that
Johan de Witt Johan de Witt (; 24 September 1625 – 20 August 1672), '' lord of Zuid- en Noord-Linschoten, Snelrewaard, Hekendorp en IJsselvere'', was a Dutch statesman and a major political figure in the Dutch Republic in the mid-17th century, the ...
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 Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
methods, game theory, and other tools of
financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...


Defined benefit pension plans

Defined benefit pension plans are a form of life annuity typically provided by employers or governments (such as
Social Security Welfare, or commonly social welfare, is a type of government support intended to ensure that members of a society can meet basic human needs such as food and shelter. Social security may either be synonymous with welfare, or refer specifical ...
in the United States). The size of payouts is usually determined based on the employee's years of service, age and salary.

Individual annuity

Individual annuities are insurance products marketed to individual consumers. With the complex selection of options available, consumers can find it difficult to decide rationally on the right type of annuity product for their circumstances.Longevity Insurance: A Missing Market
Adam Creighton, et al. University of New South Wales AU

Deferred annuity

There are two phases for a deferred annuity: * the ''accumulation'' or ''deferral'' ''phase'' in which the customer deposits (or pays premiums) and accumulates money into an account; * the ''distribution'' or ''annuitization'' ''phase'' in which the insurance company makes income payments until the death of the annuitants named in the contract Deferred annuities grow capital by investment in the accumulation phase (or deferral phase) and make payments during the distribution phase. A ''single premium deferred annuity'' (SPDA) allows a single deposit or premium at the issue of the annuity with only investment growth during the accumulation phase. A ''flexible premium deferred annuity'' (FPDA) allows additional payments or premiums following the initial premium during the accumulation phase. The phases of an annuity can be combined in the fusion of a retirement savings and retirement payment plan: the annuitant makes regular contributions to the annuity until a certain date and then receives regular payments from it until death. Sometimes there is a life insurance component added so that if the annuitant dies before annuity payments begin, a beneficiary gets either a lump sum or annuity payments.

Immediate annuity

An annuity with only a distribution phase is an ''immediate annuity, single premium immediate annuity'' (SPIA), ''payout annuity'', or ''income annuity''. Such a contract is purchased with a single payment and makes payments until the death of the annuitant(s).

Fixed and variable annuity

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 A mutual fund is a professionally managed investment fund that pools money from many investors to purchase securities. The term is typically used in the United States, Canada, and India, while similar structures across the globe include the SICAV ...
. 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 ("subaccounts") from various money managers. This gives investors the ability to move between subaccounts 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 The U.S. Securities and Exchange Commission (SEC) is an independent agency of the United States federal government, created in the aftermath of the Wall Street Crash of 1929. The primary purpose of the SEC is to enforce the law against market ...
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.

Guaranteed annuity

A pure life annuity ceases to make payments on the death of the annuitant. A ''guaranteed annuity'' or ''life and certain annuity'', makes payments for at least a certain number of years (the "period certain"); if the annuitant outlives the specified period certain, annuity payments then continue until the annuitant's death, and if the annuitant dies before the expiration of the period certain, the annuitant's estate or beneficiary is entitled to collect the remaining payments certain. The tradeoff between the pure life annuity and the life-with-period-certain annuity is that in exchange for the reduced risk of loss, the annuity payments for the latter will be smaller.

Joint annuity

''Joint-life'' and ''joint-survivor'' annuities make payments until the death of one or both of the annuitants respectively. For example, an annuity may be structured to make payments to a married couple, such payments ceasing on the death of the second spouse. In joint-survivor annuities, sometimes the instrument reduces the payments to the second annuitant after death of the first.

Impaired life annuity

There has also been a significant growth in the development of ''impaired life'' annuities. These involve improving the terms offered due to a medical diagnosis which is severe enough to reduce life expectancy. A process of medical underwriting is involved and the range of qualifying conditions has increased substantially in recent years. Both conventional annuities and Purchase Life Annuities can qualify for impaired terms.


Valuation is the calculation of economic value or worth. Valuation of an annuity is calculated as the actuarial present value of the annuity, which is dependent on the
probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking ...
of the annuitant living to each future payment period, as well as the interest rate and timing of future payments.
Life table In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, what the probability is that a person of that age will die before their next birthday ("probability of deat ...
s provide the probabilities of survival necessary for such calculations.

Annuities by region

United States

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, an Individual Retirement Account (IRA), and uses some or all of the money to buy an annuity whose payments will replace the retiree's wage payments for the rest of his/her life. 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 (income drawdown), 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.

United Kingdom

In the United Kingdom conversion of pension income into an annuity was compulsory by the age of 75 until new legislation was introduced by the coalition government in April 2011. The new rules allow individuals to delay the decision to purchase an annuity indefinitely. In the UK there are a large market of annuities of different types. The most common are those where the source of the funds required to buy the annuity is from a pension scheme. Examples of these types of annuity, often referred to as a Compulsory Purchase Annuity, are conventional annuities, with profit annuities and unit linked, or "third way" annuities. Annuities purchased from savings (i.e. not from a pension scheme) are referred to as Purchase Life Annuities and Immediate Vesting Annuities. In October 2009, the International Longevity Centre-UK published a report on Purchased Life Annuities (Time to Annuitise). In the UK it has become common for life companies to base their annuity rates on an individual's location. Legal & General were the first company to do this in 2007.


In Canada the most common type of annuity is the life annuity, which is normally purchased by persons at their retirement age with tax-sheltered funds or with savings funds. The monthly payments from annuities with tax-sheltered funds are fully taxable when withdrawn as neither the capital or return thereon has been taxed in any way. Conversely income from annuities purchased with savings funds is divided between the return of capital and interest earned, with only the latter being taxable. An annuity can be a single life annuity or a joint life annuity where the payments are guaranteed until the death of the second annuitant. It is regarded as ideal for retirees as it is the only income of any financial product that is fully guaranteed. In addition, while the monthly payments are for the upkeep and enjoyment of the annuitants, any guaranteed payments on non-registered annuities are continued to beneficiaries after the second death. This way the balance of the guaranteed payments supports family members and becomes a two-generation income.


Some countries developed more options of value for this type of instrument than others. However, a 2005 study reported that some of the risks related to
longevity The word " longevity" is sometimes used as a synonym for "life expectancy" in demography. However, the term ''longevity'' is sometimes meant to refer only to especially long-lived members of a population, whereas ''life expectancy'' is always d ...
are poorly managed "practically everywhere" due to governments backing away from defined benefit promises and insurance companies being reluctant to sell genuine life annuities because of fears that life expectancy will go up. Longevity insurance is now becoming more common in the UK and the U.S. (see Future of annuities, below) while Chile, in comparison to the U.S., has had a very large life annuity market for 20 years.

Future of annuities

It is expected that the aging of the
baby boomer Baby boomers, often shortened to boomers, are the Western demographic cohort following the Silent Generation and preceding Generation X. The generation is often defined as people born from 1946 to 1964, during the mid-20th century baby boom. ...
generation in the US will increase the demand for this type of instrument and for it to be optimized for the annuitant. This growing market will drive improvements necessitating more research and development of instruments and increase insight into the mechanics involved on the part of the buying public. An example of increased scrutiny and discussion is that related to
privatization Privatization (also privatisation in British English) can mean several different things, most commonly referring to moving something from the public sector into the private sector. It is also sometimes used as a synonym for deregulation when ...
of part of the U.S.
Social Security Trust Fund The Federal Old-Age and Survivors Insurance Trust Fund and Federal Disability Insurance Trust Fund (collectively, the Social Security Trust Fund or Trust Funds) are trust funds that provide for payment of Social Security (Old-Age, Survivors, and D ...
. In late 2010, discussions related to cutting Federal taxes raised anew the following concern: how much would an annuity cost a retiree if he or she had to replace his or her Social Security income? Assuming that the average benefit from Social Security is $14,000 per year, the replacement cost would be about $250,000 for a 66-year-old individual. The figures are based upon the individual receiving an inflation-adjusted stream that would pay for life and be insured.Could you retire without Social Security?
Bret Arends, WSJ

European Court of Justice ruling

In March 2011 a European Court of Justice ruling was made that prevents annuity providers from setting different premiums for men and women. Annuity rates for men are generally higher than those for women because men, on average, have shorter life expectancies. The change means that either annuity rates for men will fall, annuity rates for women will rise, or a combination of both. In the UK any annuities that are taken out after 21 December 2012 will have to comply with the ruling.

See also

* Annuity (European financial arrangements)#Life annuity * Certificate of life * Tontine * Life estate



External links

Math and spreadsheet for purchase and deferral decision

Retirement Annuities Actuarial science