Annuities

Definition

Annuities are financial products that provide regular payments over time, typically used for retirement income. Their value can be analyzed using calculus concepts such as series and integrals.

5 Must Know Facts For Your Next Test

1. The present value of an annuity can be calculated using the formula $PV = \sum_{n=1}^{N} \frac{C}{(1 + r)^n}$, where $C$ is the cash flow, $r$ is the discount rate, and $N$ is the number of periods.
2. Annuities can be classified into ordinary annuities (payments made at the end of each period) and annuities due (payments made at the beginning of each period).
3. In calculus, annuities often utilize geometric series for their valuation.
4. The future value of an annuity can be found using the formula $FV = C \cdot \frac{(1 + r)^N - 1}{r}$.
5. Continuous annuities involve integrating a function to determine total value over time.

Review Questions

• What is the difference between an ordinary annuity and an annuity due?
• How do you calculate the present value of an annuity using a power series?
• What role does integration play in evaluating continuous annuities?

Related terms

Geometric Series: A series with a constant ratio between successive terms.

Present Value: The current worth of a sum of money to be received in the future, discounted at a specific interest rate.

Future Value: $FV = PV(1 + r)^N$, where $PV$ is present value, $r$ is interest rate, and $N$ is number of periods.