- published: 29 Sep 2014
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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 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.
Examples of annuities are regular deposits to a savings account, monthly home mortgage payments and monthly insurance payments. Annuities are classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other interval of time.
An ordinary annuity (also referred as annuity-immediate) is an annuity whose payments are made at the end of each period (e.g. a month, a year). The values of an annuity immediate with level periodic payments can be calculated through the following:
Let:
Then the accumulated value at time t of the n payments of amount R is:
Also:
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An Annuity is any continuing payment with a fixed total annual amount. Annuity may refer to:
An annuity that has no definite end is called a perpetuity.
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory.
For example, $100 of today's money invested for one year and earning 5% interest will be worth $105 after one year. Therefore, $100 paid now or $105 paid exactly one year from now both have the same value to the recipient who assumes 5% interest; using time value of money terminology, $100 invested for one year at 5% interest has a future value of $105. This notion dates at least to Martín de Azpilcueta (1491–1586) of the School of Salamanca.
The method also allows the valuation of a likely stream of income in the future, in such a way that the annual incomes are discounted and then added together, thus providing a lump-sum "present value" of the entire income stream.
All of the standard calculations for time value of money derive from the most basic algebraic expression for the present value of a future sum, "discounted" to the present by an amount equal to the time value of money. For example, a sum of FV to be received in one year is discounted (at the rate of interest r) to give a sum of PV at present: PV = FV − r·PV = FV/(1+r).
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