Annuities can turn lump sums or periodic investments into a predictable stream of guaranteed income. They can be a powerful retirement planning tool, made even more valuable when you understand the true worth of an annuity using a few basic annuity and finance formulas. 

The present value of annuity formula (PV) tells you what your future annuity payments are worth today. The future value of annuity formula (FV) shows how your investment can grow over time, factoring in compound interest. 

These formulas help determine how much income an annuity can generate, how much you need to invest or contribute to make it happen, and how interest rates and payment schedules affect your results. 

Read on to learn more about annuity growth formulas and how to use them to estimate retirement income.

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What are annuity values, and why do they matter?

Annuity values represent how much your annuity payments are worth at different points in time. The PV of an annuity tells you how much your future payments are worth in today’s dollars, taking into account the time value of money (a discount rate, which is the rate of return you can expect to earn over time). The FV of an annuity projects how much your annuity will be worth later based on time, its growth rate, and compounding. 

These values are important for retirement planning, annuity selection, and determining how much income an annuity can provide over time. 

How to calculate the future value of an annuity

The FV formula measures the total value of annuity payments with compound interest. 

Calculating annuity growth depends on whether it’s structured as an ordinary annuity or annuity due. 

FV ordinary annuity = C × [(1 + i)^n – 1] / i

An ordinary annuity makes payments at the end of each period. 

In the formula:

• C = annuity payment per period
• i = interest rate per period
• n = number of periods

Example: If you make a $1,000 annual contribution over 5 years at 5%, the future value of your ordinary annuity equals $5,525.60

Here’s the step-by-step breakdown to use the formula:

1. Plug the numbers into the formula:
   
   FV = $1,000 × [((1 + 0.05)^5 – 1) / 0.05]
   
   
2. Calculate (1 + 0.05)^5
   
   (1 + 0.05)^5 = 1.27638
   
   
3. Subtract 1 and divide by the interest rate (0.05)
   
   $1,000 × [0.27628 / 0.05]
   
   
4. Multiply the result by the payment per period:
   
   $1,000 × 5.5256 = $5,525.60

FV annuity due = C × [(1 + i)^n – 1] / i × (1 + i)

An annuity due makes payments at the beginning of each period, giving each payment an extra compounding period. 

Using the same example and putting our numbers into the annuity due formula, our result is $5,801.91. 

Here’s the step-by-step breakdown to use the formula:

1. Plug the numbers into the formula:

FV = $1,000 × [(1 + 0.05)^5 – 1] / 0.05 × (1 + 0.05)

2. Calculate [(1 + 0.05)^5 – 1] / 0.05
   
   [(1 + 0.05)^5 – 1] / 0.05 = 5.52563
   
   
3. Multiply this result by (1 + 0.05)
   
   5.52563 × (1 + 0.05) = 5.80191
   
   
4. Multiply the result by the payment per period:
   
   $1,000 × 5.80191 = $5,801.91

This confirms that the annuity due grows more than the ordinary annuity because you’re investing your money for longer. This allows the interest to grow more.

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How to calculate annuity payments using formulas

You can also reverse these formulas to determine how much you need to contribute now to reach a future goal or income stream.

If you know the present value or future value you want, you can use these formulas to calculate annuity payments:

• From the present value formula: C = PV / [1 – (1 + i)^ – n] / i
• From the future value formula: C = FV / [(1 + i)^n – 1] / i

If you want to have $5,000 in 5 years at 5% — future value — you can reverse engineer the future value formula with your numbers and determine how to get there. 

• FV = $5,000
• n = 5
• i = 0.05 (5%)

Here’s the math:

C = FV / [(1 + i)^n – 1] / i

C = $5,000 / [(1 + 0.05)^5 – 1] / 0.05

1. Solve what is within the brackets and your result is 5.5256: 
   
   1. 1.05⁵ = 1.2762815625
   2. 1.2762815625 – 1 = 0.2762815625
   3. 0.2762815625 / 0.05 = 5.52563125
      
2. Divide your future value ($5,000) by 5.5256 (rounded) and you end up with $904.89

The math results in $904.89, meaning you would need to contribute this amount every year for 5 years to end up with $5,000 in your annuity.

Key considerations when applying annuity formulas

It’s important to keep the following considerations top of mind when you run these formulas: 

• Interest rates and compounding: Small interest rate changes impact the PV and FV of your annuity. Check to see if your annuity compounds interest annually, monthly, or quarterly.
• Payment timing: Whether you have an ordinary annuity or annuity due can impact your results. Annuity due structures can yield higher growth due to earlier payments. 
• Fixed and variable annuities: A fixed annuity has a set interest rate, offering predictable interest growth. With a variable annuity, you have to make more assumptions because of how your underlying investments fluctuate as the market moves.
• Inflation: Even if your annuity is growing, inflation can eat away at its gains. You can get a more accurate rate of return by subtracting the anticipated inflation rate.
• Calculators vs. working with advisors: Annuity calculators save you the hassle of doing the math yourself. But a financial advisor can go further and provide a better understanding of how annuities fit in your overall retirement plan.

Take control of your retirement planning with Gainbridge

Annuities can help alleviate the fear that you will outlive your money or have nothing left to support your heirs. Understanding PV and FV formulas helps you structure annuities accordingly to reach your retirement goals. 

Gainbridge digital-first annuities make it straightforward to lock in competitive interest rates — with no hidden fees or commissions. Our licensed agents can help you run the numbers with an annuity calculator so you can plan with confidence. 

Explore Gainbridge now to choose the right annuity for your retirement plan. 

‍This article is intended for informational purposes only. It is not intended to provide, and should not be interpreted as, individualized investment, legal, or tax advice. For advice concerning your own situation please contact the appropriate professional. The GainbridgeⓇ digital platform provides informational and educational resources intended only for self-directed purposes.