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Annuity (financial contracts)

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Title: Annuity (financial contracts)  
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Subject: Gerolamo Cardano, Insurance, Actuary, Pension, Frans Hals, Mary of Teck, Jean le Rond d'Alembert, Ernst & Young, Henry Benedict Stuart, Tooele County, Utah
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Annuity (financial contracts)

A life annuity is a financial contract in the form of an insurance product according to which a seller (issuer) — typically a financial institution such as a life insurance company — makes a series of future payments to a buyer (annuitant) in exchange for the immediate payment of a lump sum (single-payment annuity) or a series of regular payments (regular-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. Annuities can be purchased to provide an income during retirement, or originate from a structured settlement of a personal injury lawsuit.


The instrument's evolution has been long and continues as part of actuarial science.[1] Medieval German and Dutch cities and monasteries raised money by the sale of life annuities, and it was recognized that pricing them was difficult.[2] The early practice for selling this instrument did not consider the age of the nominee, thereby raising interesting concerns.[3] These concerns got the attention of several prominent mathematicians[4] over the years, such as Huygens, Bernoulli, de Moivre and others:[3] even Gauss and Laplace had an interest in matters pertaining to this instrument.[5] 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%.[6] Here is a quick comparison table of early life annuity prices:

Head age (x) Value of a unit annuity

ca. 200 AD

de Witt


Hôtel Dieu

ca. 1680





1 30 16 n/a 10,28 n/a
10 30 15,19 n/a 13,44 16,25
20 28 13,83 20 12,78 15,58
30 22 12,22 20 11,72 14,84
40 19 10,39 15 10,57 13,62
50 9 8,68 12 9,21 11,58
60 5 6,70 10 7,60 9,24
70 5 3,77 8 5,32 6,36
80 5 0 8 3,05 3,86
90 5 0 6 1,74 1,58
95 5 0 n/a 1,02 0
Values are approximated

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.

Phases of an annuity

There are two possible phases for an annuity:

  • The accumulation phase in which the customer deposits and accumulates money into an account, and ;
  • The distribution phase in which the insurance company makes income payments until the death of the annuitants named in the contract.

It is possible to structure an annuity contract so that it has only the distribution phase; such a contract is called an immediate annuity.

Annuity contracts with a deferral phasedeferred annuities—are essentially two-phase annuities, but only having growth of capital by investment in the accumulation phase (now the deferral phase), with no customer deposits.

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.

Decision to defer or not

The option to defer purchase of an annuity (choosing income drawdown instead) has the benefit of investment flexibility, offset by the lower annuity which one will be able to purchase later after having drawn down the capital (mortality drag). Interest rates and inflation can affect the decision to purchase, as they are reflected in the annuity rates, and also affect secure investment potential by varying bond yields. Inflation deteriorates the buying power of an annuity and can therefore be a concern, however inflation-indexed plans have been marketed.[7]

Types of life annuity

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.[7]

Fixed and variable annuities

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 ("subaccounts") from various money managers. This gives investors the ability to move between subaccounts without incurring additional fees or sales charges.

Guaranteed annuities

With a "pure" life annuity, annuitants may die before recovering the value of their original investment in it. If the possibility of this situation, called a "forfeiture," is not desired, it can be ameliorated by the addition of an added clause, forming a type of guaranteed annuity, under which the annuity issuer is required to make annuity 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 annuities

Multiple annuitant products include joint-life and joint-survivor annuities, where payments stop upon 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 annuities

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.

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.

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.[8] 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.[9]


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 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.[7] Longevity insurance is now becoming more common in the UK and the U.S. (see Future of annuites, below) while Chile, in comparison to the U.S., has had a very large life annuity market for 20 years.[10]

Future of annuities

It is expected that the aging of the baby boomer generation in the US will increase the demand for this type of instrument and for it to be optimized for the annuitant.[11] 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 of part of the U.S. Social Security Trust Fund.

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 their 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.[12]

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 they have shorter life expectancies. The change means that either annuity rates for men will fall or annuity rates for women will rise since they were not equal before the change. Typically in insurance the worse rates, those currently paid to women will be charged where separate rates are not allowed in order to avoid a situation where an individual who is undercharged can exploit the insurers.

In the UK any annuities that are taken out after 21 December 2012 will have to comply with the ruling.

See also


External links

  • Math and spreadsheet for purchase and deferral decision
  • Variable Annuities Interview- Legal Perspectivede:Leibrente

fr:Rente viagère nl:Lijfrente pl:Umowa renty fi:Elinkorko

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