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.

Ordinary Annuity

---

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 present value of an ordinary annuity can be calculated through the formula

$PV\; \backslash \; =\; \backslash \; A\; \backslash cdot\; \{\; 1\; -\; \{\; 1\; \backslash over\; (1+r)^n\; \}\; \backslash over\; r\; \}$

The future value of an ordinary annuity can be calculated through the formula

$FV\; \backslash \; =\; \backslash \; A\; \backslash cdot\; \{\; (1+r)^n\; -\; 1\; \backslash over\; r\; \}$

In each of these formulae, A is the periodic amount of the annuity, r is the period interest rate, and n is the number of periods

Annuity Due

---

An annuity-due is an annuity whose payments are made at the beginning of each period.

Because each annuity payment is allowed to compound for one extra period, the value of an annuity-due is equal to the value of the corresponding ordinary annuity multiplied by (1+r). Thus, the present value of an annuity-due can be calculated through the formula

$PV\; \backslash \; =\; \backslash \; A\; \backslash cdot\; \{\; 1\; -\; \{\; 1\; \backslash over\; (1+r)^n\; \}\; \backslash over\; r\; \}\; \backslash cdot\; (1+r)$

The future value of an of annuity-due can be calculated through the formula

$FV\; \backslash \; =\; \backslash \; A\; \backslash cdot\; \{\; (1+r)^n\; -\; 1\; \backslash over\; r\; \}\; \backslash cdot\; (1+r)$

Another intuitive way to interpret an annuity-due is as the sum of one annuity payment now (at time = 0) and an ordinary annuity without an annuity payment at the end of the last period (e.g. n-1).

=Finding Annuity Values with a Financial Calculator=

Texas Instruments BA II Plus Professional

To calculate present value of an ordinary annuity, with an annual payment of $2000 for 10 years and an interest rate of 5%

{|class="wikitable"

! To Press Display Set all variables to defaults ^* RST 0.00 Enter number of payments 10 ^* N= 10.00< Enter interest rate per payment period 5 ^* I/Y= 5.00< Enter payment 2000 ^* PMT= 2,000.00< Compute present value [PV PV= 15443.47 note: Press ^*" target="_blank" >[PV to calculate the future value

To calculate present value of an annuity due, with an annual payment of $2000 for 10 years and an interest rate of 5%

{|class="wikitable"

! To Press Display Set all variables to defaults ^* RST 0.00 Enter number of payments 10 ^* N= 10.00< Enter interest rate per payment period 5 ^* I/Y= 5.00< Enter payment 2000 ^* PMT= 2,000.00< Set beginning-of-period payments ^*" target="_blank" >[SET BGN Return to calculator mode [QUIT 0.00 Compute present value [PV PV= 16215.64 note: Press ^*" target="_blank" >[PV to calculate the future value(1)

=References=

• (1) Texas Instruments BA II Plus Guide Book

=Related Terms=

• Annuity formula
• Perpetuity
• Variable Annuity
• Deferred Annuity

=External links=

• Annuities: Ordinary? Due? What Do I Do? -- Annuity tutorial (with quiz) from Prof. John Wachowicz at the University of Tennessee.
• Edmond Halley, An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives, Philosophical Transactions, 196 (London, 1693), p.596-610.
• Non-commercial webform to calculate annuities

Annuität | Annuita