Annuity

Definition

An annuity is a sequence of equal payments made at regular intervals over time. In algebra, it is often analyzed using series and their notations to understand the accumulation of payments.

5 Must Know Facts For Your Next Test

1. Annuities can be classified as either ordinary (payments made at the end of each period) or annuities due (payments made at the beginning of each period).
2. The future value of an annuity can be calculated using the formula $FV = P \left(\frac{(1 + r)^n - 1}{r}\right)$ where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods.
3. The present value of an annuity can be calculated with $PV = P \left(\frac{1 - (1 + r)^{-n}}{r}\right)$.
4. Geometric series are often used to derive formulas for both present and future values of annuities.
5. Understanding annuities involves concepts from sequences, such as recognizing arithmetic sequences in payment schedules.

Review Questions

• What distinguishes an ordinary annuity from an annuity due?
• How do you calculate the future value of an annuity given regular payments, interest rate, and number of periods?
• Explain how geometric series are used in calculating annuities.

Related terms

Geometric Series: A series with a constant ratio between successive terms. Used in calculating present and future values of annuities.

Present Value: The current worth of a stream of cash flows given a specified rate of return or discount rate.

Future Value: The value of a current asset at a specified date in the future based on an assumed rate of growth or interest.