Future Value of Annuity Calculator
See how a stream of equal payments grows over time. Supports ordinary annuities and annuities due with flexible payment and compounding frequencies.
Future Value of Annuity
How this future value of annuity calculator works
This tool calculates how much a series of equal payments will be worth at a future date, given a constant interest rate. It supports:
- Ordinary annuity – payments at the end of each period (most loans, many investments).
- Annuity due – payments at the beginning of each period (rent, many retirement contributions).
- Different payment frequencies (monthly, weekly, etc.).
- Different compounding frequencies (monthly, daily, etc.).
Formulas for future value of an annuity
1. Ordinary annuity (end-of-period payments)
Formula:
\[ FV_{\text{ordinary}} = P \times \frac{(1 + r)^n - 1}{r} \]
where:
- \(FV_{\text{ordinary}}\) = future value of the annuity
- \(P\) = payment per period
- \(r\) = interest rate per period
- \(n\) = total number of periods
2. Annuity due (beginning-of-period payments)
Formula:
\[ FV_{\text{due}} = FV_{\text{ordinary}} \times (1 + r) \]
or directly:
\[ FV_{\text{due}} = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r) \]
3. Matching payments and compounding
In many real products, payments and compounding do not happen at the same frequency. To handle this correctly, the calculator:
- Converts the annual rate to an effective rate per compounding period.
- Simulates each period, applying interest and adding payments at the right times.
This makes the results more realistic than a simple closed-form formula that assumes matching frequencies.
Example: Monthly savings into a retirement account
Suppose you:
- Invest $500 per month.
- Earn 6% annual interest, compounded monthly.
- Contribute for 20 years.
- Make payments at the end of each month (ordinary annuity).
Then:
- \(P = 500\)
- \(r = 0.06 / 12 = 0.005\)
- \(n = 20 \times 12 = 240\)
\[ FV_{\text{ordinary}} = 500 \times \frac{(1 + 0.005)^{240} - 1}{0.005} \]
Enter these values in the calculator to see the exact future value, total contributions, and interest earned.
Future value of annuity vs. present value
The future value of an annuity tells you how much your payments will grow to in the future. The present value of an annuity tells you how much that future stream of payments is worth today.
Lenders and insurers often quote products in terms of present value, while savers and investors are usually more interested in future value. Both are linked by the same interest rate and time horizon.
Common use cases
- Retirement planning: Estimate how much regular contributions will grow to by retirement age.
- Education savings: Plan monthly deposits into a college fund.
- Saving for a goal: Build a down payment, emergency fund, or other target amount.
- Comparing products: Compare the future value of different savings or annuity contracts.
Limitations and assumptions
- Assumes a constant interest rate over the entire period.
- Assumes equal payments at regular intervals.
- Ignores taxes, fees, and inflation unless you adjust the rate accordingly.
In reality, interest rates and contributions may change over time. Use this calculator as a planning tool, not a guarantee of future returns.
FAQ: Future value of an annuity
Is an annuity due always better than an ordinary annuity?
For the same payment amount, interest rate, and number of payments, an annuity due will always have a higher future value than an ordinary annuity, because each payment has one extra period to earn interest. However, many products price this in, so you should compare overall terms, not just timing.
What interest rate should I use?
Use the expected annual return of your investment after fees. For bank savings, this is usually the quoted APY or interest rate. For long-term investing in diversified portfolios, people often use historical averages (e.g., 5–8% per year), but future returns are uncertain.
Can I handle changing contributions?
This calculator assumes a fixed payment per period. To approximate changing contributions, you can:
- Run separate calculations for each phase (e.g., $200/month for 5 years, then $400/month for 10 years).
- Add the resulting future values together.