Annuity (financial contracts)

A life annuity is an annuity, or series of payments at fixed intervals, paid while the purchaser (or annuitant) is alive. A life annuity is an insurance product typically sold or issued by life insurance companies. 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. 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.

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%.

...
Wikipedia