# Future Value of Annuity: Calculation Formulas & Key Insights

![Future Value of an Annuity: The value of a group of recurring payments at a certain date in the future.](https://www.investopedia.com/thmb/2YEfSbJA3JW9PeDdrE1aKzYOwYw=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/FutureValueofanAnnuity_final-05f2d1d9409646adb05be26c49787a26.png)

*— Investopedia / Michela Buttignol*

> **Definition**
>
> The future value of an annuity calculates how much a series of payments is worth in the future given a specified interest or discount rate.

## What Is the Future Value of an Annuity?

The future value of an annuity is how much recurring payments will be worth at a future date, based on a specified rate of return or [discount rate](https://www.investopedia.com/terms/d/discountrate.asp).

A higher discount rate increases the future value of the annuity. 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](https://www.investopedia.com/retirement/calculating-present-and-future-value-of-annuities/).

### Key Takeaways

*   The future value of an annuity is calculated using a formula that requires knowing the annuity payment amount, number of periods, and projected rate of return.  
    
*   An ordinary annuity involves payments made at the end of each period, while an annuity due involves payments made at the beginning, resulting in a higher future value for annuities due.  
    
*   Understanding the future value of an annuity helps in assessing the growth potential of recurring payments over time, emphasizing the impact of the time value of money.  
    
*   The formula for calculating the future value differs between ordinary annuities and annuities due, with an extra compounding period for annuities due.

## Exploring the Future Value of an Annuity

Due to the time value of money, money today is worth more than the same amount in the future. That's because the money can be invested and allowed to grow over time. Similarly, a $5,000 lump sum today is worth more than five $1,000 annuity payments over five years.

## How to Calculate the Future Value of an Annuity

The formula for the future value of an [ordinary annuity](https://www.investopedia.com/terms/o/ordinaryannuity.asp) 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](https://www.investopedia.com/terms/a/annuitydue.asp).)

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

> **Important**
>
> While ordinary annuities are more common, annuities due usually have a higher future value, assuming other conditions are constant.

## Practical Example: Calculating Future Value of an Annuity

With an annuity due, payments are made at the beginning of each period. So the formula is slightly different. To calculate the future value of an annuity due, multiply the ordinary annuity formula by (1 + r).

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

## Calculating the Future Value of an Annuity Due

Let's say someone decides to invest $125,000 per year for the next five years in an annuity that they expect to [compound](https://www.investopedia.com/terms/c/compoundinterest.asp) 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](https://www.investopedia.com/ask/answers/070915/what-difference-between-present-value-annuity-and-future-value-annuity.asp) 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

Let's use the same example as above, but with an annuity due. This means that 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 the money 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](https://www.investopedia.com/terms/f/futurevalue.asp) factor. The future value factor is the aggregated growth that a [lump sum](https://www.investopedia.com/terms/l/lump-sum-payment.asp) 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 typically made at the end of a period. An annuity due, however, is a payment that is 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](https://www.investopedia.com/ask/answers/070915/what-difference-between-present-value-annuity-and-future-value-annuity.asp) 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](https://www.investopedia.com/terms/s/stock.asp) today for $100 that awards a 2% dividend each year, you can calculate the future value of that stock. Alternatively, if you want to have $10,000 of future value on hand for [a down payment for a car](https://www.investopedia.com/how-much-down-payment-is-needed-for-a-car-5184453) 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 as to whether the annuity payments are made at the beginning or at the end of a period.