# Future Value of an Annuity: What Is It, Formula, and Calculation

## What Is the Future Value of an Annuity?

The future value of an annuity is the value of a group of recurring payments at a certain date in the future, assuming a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value. As long as all of the variables surrounding the annuity are known such as payment amount, projected rate, and number of periods, it is possible to calculate the future value of the annuity.

### Key Takeaways

• The future value of an annuity is a way of calculating how much money a series of payments will be worth at a certain point in the future.
• By contrast, the present value of an annuity measures how much money will be required to produce a series of future payments.
• In an ordinary annuity, payments are made at the end of each agreed-upon period. In an annuity due, payments are made at the beginning of each period.
• To calculate the future value of an annuity, you must know the annuity payment amount, number of periods, and projected rate of return.
• Because annuity due payments often entail having an additional compounding period, the future value of an annuity due will usually be higher than the future value of an annuity.

## Understanding the Future Value of an Annuity

Because of the time value of money, money received or paid out today is worth more than the same amount of money will be in the future. That's because the money can be invested and allowed to grow over time. By the same logic, a lump sum of $5,000 today is worth more than a series of five$1,000 annuity payments spread out over five years.

Ordinary annuities are more common, but an annuity due will result in a higher future value, all else being equal.

## Formula and Calculation of the Future Value of an Annuity

The formula for the future value of an ordinary annuity is as follows. (An ordinary annuity pays interest at the end of a particular period, rather than at the beginning, as is the case with an annuity due.)

\begin{aligned} &\text{P} = \text{PMT} \times \frac { \big ( (1 + r) ^ n - 1 \big ) }{ r } \\ &\textbf{where:} \\ &\text{P} = \text{Future value of an annuity stream} \\ &\text{PMT} = \text{Dollar amount of each annuity payment} \\ &r = \text{Interest rate (also known as discount rate)} \\ &n = \text{Number of periods in which payments will be made} \\ \end{aligned}

### Future Value of an Annuity Due

With an annuity due, where payments are made at the beginning of each period, the formula is slightly different. To find the future value of an annuity due, simply multiply the formula above by a factor of (1 + r). So:

\begin{aligned} &\text{P} = \text{PMT} \times \frac { \big ( (1 + r) ^ n - 1 \big ) }{ r } \times ( 1 + r ) \\ \end{aligned}

## Future Value of an Annuity Example

Assume someone decides to invest 125,000 per year for the next five years in an annuity they expect to compound at 8% per year. In this example, the series of payments is a regular annuity in which the payments are made at the end of each period. The expected future value of this payment stream using the above formula is as follows: \begin{aligned} \text{Future value} &= \125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \\ &= \733,325 \\ \end{aligned} ### Future Value of an Annuity Due Assume the same example as above was an annuity due. This means each of the125,000 payments was made at the beginning of each period. Its future value would be calculated as follows:

\begin{aligned} \text{Future value} &= \125,000 \times \frac { \big ( ( 1 + 0.08 ) ^ 5 - 1 \big ) }{ 0.08 } \times ( 1 + 0.08 ) \\ &= \791,991 \\ \end{aligned}

## The Bottom Line

An annuity is a series of payments made over a period of time, often for the same amount each period. Investors can determine the future value of their annuity by considering the annuity amount, projected rate of return, and number of periods. There are also implications whether the annuity payments are made at the beginning of the period or at the end.

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