## 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 the $125,000 payments was made at the beginning of each period. Its future value would be calculated as follows:

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

All else being equal, the future value of an annuity due will be greater than the future value of an ordinary annuity because it has had an extra period to accumulate compounded interest. In this example, the future value of the annuity due is $58,666 more than that of the ordinary annuity.

## What Is a Future Value Factor?

When calculating future values, one component of the calculation is called the future value factor. The future value factor is simply the aggregated growth that a lump sum or series of cash flow will entail. For example, if the future value of $1,000 is $1,100, the future value factor must have been 1.1. A future value factor of 1.0 means the value of the series will be equal to the value today.

## What Is The Difference Between Annuity and Annuity Due?

Annuity payments are often made at the end of a period. An annuity due, however, is a payment made at the beginning of a period. Though it may not seem like much of a distinction, there may be considerable differences between the two when considering what interest is accrued.

## What Is the Relationship Between Present Value and Future Value?

Present value and future value simply indicate the value of an investment looking forward or looking back. The two concepts are directly related, as the future value of a series of cash flows also has a present value. For example, a present value of $1,000 today may be equal to the future value of $1,200 today.

Most often, investors and analysts will know one value and try to solve for the other. For instance, if you buy a stock today for $100 that awards a 2% dividend each year, you can calculate the future value. Alternatively, if you want to have $10,000 of future value on hand for a down payment for a car next year, you can solve for the present value.

## 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.