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The term annuity is used in finance theory to
refer to any terminating stream of fixed payments over a specified period of
time. This usage is most commonly seen in academic discussions of finance,
usually in connection with the valuation of the stream of payments, taking
into account time value of money concepts such as interest rate and future
value.[1]

The life annuity is a financial contract according to which a seller
(issuer) - typically a financial institution such as a life insurance
company - makes a series of payments in the future to the buyer (annuitant)
in exchange for the immediate payment of a lumpsum (in the case of a
single-payment annuity) or a series of payments prior to the return
payments.
The payment stream from the issuer to the
annuitant has an unknown duration based principally upon the date of death
of the annuitant: it generally stops then. However, it is possible to
structure a life annuity so that the payments instead only stop upon the
death of a second of two annuitants (i.e., a joint and survivor annuity);
sometimes the instrument reduces the payments to the second annuitant.

The risks of such a situation, called a
"forfeiture", can be ameliorated by the addition of an added clause 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.

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