## Future Value of Annuity Due

The future value of an annuity due refers to the value of a series of recurring, equal payments (annuity) at some date in the future, assuming the payments are made at the beginning of each period. This differs from a standard (or ordinary) annuity, where payments are made at the end of the period.

The future value of an annuity due can be calculated using the following formula:

\(FV = P \times \frac{(1 + r)^n – 1}{r} \times (1 + r) \)

Where:

- FV = Future Value
- P = Payment amount per period
- r = interest rate per period
- n = total number of payments (or periods)

The (1 + r) term at the end of the formula accounts for the fact that each payment is compounded for one additional period compared to a standard annuity.

## Example of Future Value of Annuity Due

Suppose you plan to deposit $500 at the beginning of each year into a savings account that pays an annual interest rate of 4%. You plan to do this for 6 years.

The future value of an annuity due can be calculated using the following formula:

\(FV = P \times \frac{(1 + r)^n – 1}{r} \times (1 + r) \)

where:

- FV = Future Value
- P = Payment amount per period
- r = interest rate per period
- n = total number of payments (or periods)

For this example, the values are:

- P = $500
- r = 0.04
- n = 6

Substitute these values into the formula:

\(FV = \$500 \times \frac{(1 + 0.04)^6 – 1}{0.04} \times (1 + 0.04) \)

\(= \$500 \times \frac{1.265319 – 1}{0.04} \times (1 + 0.04) \)

\(= \$500 \times \frac{0.265319}{0.04} \times (1 + 0.04) \)

\(= \$3,316.4875 \times 1.04 \)

= $3,447.147

So, the future value of the annuity due (the amount you’ll have in your savings account after 6 years) would be approximately $3,447.15. This calculation shows the power of compound interest and regular saving over time.