How to calculate the future value of an annuity

If you receive $10,000 today, it’s worth more than receiving a set of 10, $1,000 payments annually. This is because, over time, inflation decreases the value — the purchasing power — of money. Therefore, it’s important to calculate the future value of an annuity before purchasing. 

Read on to learn how to calculate the present versus future value of an annuity so you better understand your annuity’s trajectory. 

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What’s the future value of an annuity?

The future value of an annuity quantifies how much your periodic payments will be worth in the future. To achieve the overarching goal of having enough money to live comfortably in retirement, you want the future value of your annuity to be worth more than its present value. 

Present versus future value of an annuity

The future value of an annuity is worth more than its present value because, through additional contributions and interest earned, your annuity grows on a compounding basis. 

Think of present value the opposite way: It determines how much money you must contribute today to realize a desired outcome tomorrow, factoring in a fixed (or anticipated, if a variable annuity) rate of return over the life of your annuity. 

That’s why the future value should always be worth more than the present value. So, if you want to have $6,500 in 10 years (future value), you would need to deposit $5,000 today (present value) and achieve an annual average rate of return of 5.5% to get there. 

Understanding future value of an annuity formula

When you earn interest, this money gets added to your principal deposit. As this process takes hold, your annuity company calculates subsequent interest payments on this new (principal + interest) total. So you’re earning interest on your interest, your original contribution, and any new money contributions. 

The future value of an annuity takes this into account to help you visualize how much the money you’re contributing, alongside compounding, will be worth when you need it. 

Ordinary annuity vs. annuity due

A lot affects the future annuity calculation, like whether you have an ordinary annuity versus an annuity due: 

• Ordinary annuity: Your annuity payments are due at the end of each period, which means your money has less time to accrue interest (so likely a lower future value).
• Annuity due: Your payments are due at the beginning of each period, which means your money has more time to earn interest (so likely a higher future value).

How to calculate the future value of an annuity

With all this complexity in mind, let’s look at the data you need to calculate the future value of your annuity: 

• PMT: The amount of money you contribute in your annuity at each interval. This number can be a lump sum deposit only or your initial deposit plus ongoing contributions.
• r: Your interest rate, sometimes called the discount rate. 
• n: The number of payments you’ll make during the accumulation phase.

How to calculate the future value of an ordinary annuity

Here’s the future value of an ordinary annuity formula:

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PMT x [ ([1 + r]^n – 1) / r]

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Now let’s use it — consider a basic contribution of $5,000 per year, every year, for 10 years, at a 5.5% interest rate. 

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FV = $5,000 x [([1 + 0.055]^10 – 1) / 0.055]

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And let’s calculate everything to find the future value (FV):

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Calculate (1 + 0.055)^10:

(1 + 0.055)^10 = 1.7081

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Subtract 1 and divide by the interest rate (0.055):

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(1.7081 – 1) / 0.055 = 12.8745

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Multiply the result by the payment per period:

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$5,000 x 12.8745 = 64,372.50

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So: You contributed $50,000 of new money ($5,000 each year for 10 years) at an interest rate of 5.5%. Thanks to compounding growth, your $50,000 in deposits turns into $64,372 and change after the 10-year accumulation phase. 

How to calculate the future value of an annuity due

The future value of an annuity due formula looks like this:

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PMT x [ ([1 + r]^n – 1) x (1 + r) / r]

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We’ll use the same input as we used in the above example — let’s plug the numbers into the above formula:

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FV = $5,000 x [ ([1 + 0.055]^10 – 1) x (1 + 0.055) / 0.055]

[((1 + 0.055)^10 – 1) / 0.055] = 12.8816

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Multiply this result by (1 + 0.055):

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12.8816 x (1 + 0.055) = 13.587

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Multiply the result by the payment per period:

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$5,000 x 13.587 = 67,935.5

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The future value of this annuity due example — taking 10 annual payments of $5,000 each at a 5.5% interest rate — is $67,935.50. 

As mentioned, you’d get back more with an annuity due than an ordinary annuity.

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How to use the future value of an annuity in real life

Let’s consider a few real-world examples to illustrate the future value of an annuity formula. 

Saving for a new car

You want to have $25,000 saved for a new car in 10 years. You can use the future value of an annuity formula to build a plan and stay on track. It shows how much you must save each month to reach your number. 

If you can generate a 5% annual rate of return, the math shows that you need to save about $161 a month over 10 years to reach $25,000. 

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Here’s how the numbers look plugged into the formula with interest compounded monthly:

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FV = $25,000

r = 0.05 / 12 = 0.004167

n = 10 × 12 = 120 months

Entered into the formula:

25,000 = P × [((1 + 0.004167)^120 - 1) / 0.004167]

25,000 = P × 155.292

P ≈ 25,000 / 155.292 ≈ $161

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You'd need to save $161 monthly to come up with $25,000 to help buy the car. 

Saving for a down payment on a house

You want to accumulate $40,000 within five years to put toward a down payment on a house. By using the future value of an annuity formula today, you save yourself the burden of taking on additional debt tomorrow.

At a 4% annual rate of return, you’ll need to save $605 a month, every month, to get to $40,000 in five years. 

Planning for retirement

You can also use this formula for longer-term goals. Imagine a 35-year-old who wants to have $500,000 for retirement by age 65. At a 6% rate of return, this person needs to save roughly $500 a month for 30 years to build a $500,000 retirement nest egg. 

The future value of an annuity formula is ideal for estimating savings over time. It calculates interest on each payment you make, with each payment generating interest over different periods. This type of compounding is powerful, and it’s part of what makes annuities great savings tools. 

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This communication is for informational purposes only. It is not intended to provide, and should not be interpreted as, individualized investment, legal, or tax advice.

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