Dated assumptions · transparent formulas
Future Value of Annuity Calculator
Project a series of equal payments with an ordinary annuity or annuity due. Choose payment frequency, interest rate, and the number of years.
Educational calculator. Inputs stay in your browser. Historical ranges are not forecasts or investment advice.
Inputs
Estimate comparison
| Assumption | Rate | Nominal FV | Real FV |
|---|---|---|---|
| Lower estimate1-year Treasury constant maturity | 4.28% | $37,361.10 | Not requested |
| Middle estimateS&P 500 rolling 30-year total-return median | 10.80% | $53,624.67 | Not requested |
| Higher estimateS&P 500 rolling 30-year total-return 75th percentile | 12.04% | $57,644.94 | Not requested |
Growth curve and yearly schedule
The same projection engine draws each estimate and feeds the collapsible year-by-year detail.
- Lower estimate
- Middle estimate
- Higher estimate
Show year-by-year detail
| Year | Opening | Deposits | Interest | Ending |
|---|---|---|---|---|
| 1 | $0.00 | $3,000.00 | $153.05 | $3,153.05 |
| 2 | $3,153.05 | $3,000.00 | $510.95 | $6,663.99 |
| 3 | $6,663.99 | $3,000.00 | $909.47 | $10,573.47 |
| 4 | $10,573.47 | $3,000.00 | $1,353.24 | $14,926.71 |
| 5 | $14,926.71 | $3,000.00 | $1,847.37 | $19,774.08 |
| 6 | $19,774.08 | $3,000.00 | $2,397.60 | $25,171.67 |
| 7 | $25,171.67 | $3,000.00 | $3,010.28 | $31,181.95 |
| 8 | $31,181.95 | $3,000.00 | $3,692.50 | $37,874.45 |
| 9 | $37,874.45 | $3,000.00 | $4,452.16 | $45,326.61 |
| 10 | $45,326.61 | $3,000.00 | $5,298.06 | $53,624.67 |
Rate assumptions and sources
Lower / Middle / Higher estimates · reviewed 2026-09-12
- Lower estimate
4.28%
- FRED: 1-Year Treasury Constant Maturity Rate (DGS1)
Retrieved 2026-09-12 · observation 2026-09-10
Dated benchmark snapshot.
- Middle estimate
10.80%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
Median of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Higher estimate
12.04%
- Damodaran historical returns, 1928-2025
Retrieved 2026-09-12
75th percentile of 69 overlapping 30-year S&P 500 total-return windows through 2025.
- Inflation: 3.34%
- FRED: Consumer Price Index for All Urban Consumers (CPIAUCSL)
Compound annual change from August 2016 to August 2026; user input can replace it.
Ordinary annuity versus annuity due
An ordinary annuity makes the same payment at the end of each period. An annuity due makes that payment at the beginning, giving every deposit one additional period to earn interest. Keep the starting balance at zero to isolate the annuity itself.
This calculator models a savings cash-flow series, not an insurance annuity contract or a guaranteed retirement payout. Taxes, fees, contract guarantees, and insurer risk are outside the projection.
If your deposits increase over time, use the growing annuity calculator. A level-payment annuity and a growing annuity have different cash-flow schedules and formulas.
Future value of an ordinary annuity formula
FV = P × ((1 + i)^n − 1) / i, where P is the equal payment, i is the effective interest rate per payment period, and n is the number of payments. When i = 0, FV = P × n.
For annuity due, multiply the ordinary annuity result by (1 + i). If there is an opening balance, add PV × (1 + i)^n separately. The default end-of-month schedule uses 120 payments over 10 years.
For monthly payments and monthly compounding, i = r / 12 and n = 12 × years. If compounding frequency differs, i = (1 + r/m)^(m/k) − 1, where m is compounds per year and k is payments per year.
Worked example: $250 a month for 10 years
With no opening balance, $250 deposited at the end of each month for 10 years, and a 6% nominal annual return compounded monthly, the future value is $40,969.84. Contributions total $30,000 and projected interest is $10,969.84.
Switching to beginning-of-month payments raises the result to $41,174.69. The extra $204.85 comes only from timing; the number and size of payments stay the same. At zero interest, either schedule reaches $30,000.
To reproduce this example, enter a starting amount of 0, a contribution of 250, monthly contributions, 10 years, monthly compounding, and a 6% rate. Leave inflation adjustment off to compare the nominal answer.
Frequently asked questions
What is the difference between an ordinary annuity and annuity due?
An ordinary annuity pays at the end of each period; an annuity due pays at the beginning. With positive interest, annuity due has a higher future value because each payment earns one extra period of interest.
Is FV of annuity the same as future value of annuity?
Yes. FV abbreviates future value. For equal payments, both names refer to the same ordinary annuity or annuity due calculation.