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.
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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.
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).
In calculus, annuities often utilize geometric series for their valuation.
The future value of an annuity can be found using the formula $FV = C \cdot \frac{(1 + r)^N - 1}{r}$.
Continuous annuities involve integrating a function to determine total value over time.