The future value of an annuity represents the total value of a series of equal payments made at regular intervals over a specified period, assuming a certain interest rate or rate of return. An annuity is a financial product that provides a series of payments over time, either received (as in the case of an income annuity) or paid (as in the case of an annuity due or ordinary annuity).

The formula for calculating the future value of an annuity (FV) is given by:

\[ FV = PMT \times \left( \frac{(1 + r)^n – 1}{r} \right) \]

Where:
– \( FV \) is the future value of the annuity.
– \( PMT \) is the periodic payment (annuity payment).
– \( r \) is the interest rate per period (expressed as a decimal).
– \( n \) is the number of periods.

This formula assumes that payments are made at the end of each period. If payments are made at the beginning of each period (annuity due), the formula is slightly modified:

\[ FV = PMT \times \left( \frac{(1 + r)^n – 1}{r} \right) \times (1 + r) \]

Let’s break down the components:

– \( (1 + r)^n – 1 \): This part calculates the future value of a series of future cash flows. It’s a factor that considers the compounding effect over the number of periods.

– \( \frac{(1 + r)^n – 1}{r} \): This part calculates the present value of the future cash flows. It represents the present value of an annuity factor, discounting the future cash flows back to their present value.

– \( PMT \times \left( \frac{(1 + r)^n – 1}{r} \right) \): This part calculates the future value of the annuity, taking into account the periodic payment.

– \( (1 + r) \): For an annuity due, this factor accounts for the compounding effect when payments are made at the beginning of each period.

**How to Calculate Future Value of an Annuity:**
1. Identify the periodic payment (PMT), which represents the equal payments made at regular intervals.
2. Determine the interest rate per period (r).
3. Specify the number of periods (n) for which you want to calculate the future value.
4. Apply the values to the appropriate formula, depending on whether the annuity payments are made at the end or beginning of each period.

This calculation is useful in financial planning, retirement planning, and other scenarios where a series of equal payments is made or received over time.