How to use the annuity calculator
Start with any balance you already have, or enter zero if the payments start from nothing. Then add the regular payment and how often you make it, from weekly to once a year.
Payment frequency and compounding frequency are separate fields. You can pay monthly into an account that compounds daily or yearly, and the calculator converts the rate to match your payment schedule.
- Enter the current value (or zero) and the payment per period.
- Pick the payment frequency and whether payments land at the end (ordinary annuity) or start (annuity due) of each period.
- Add an optional yearly extra payment and a yearly change to both payment amounts.
- Enter the nominal annual rate, how often it compounds, and the term in years.
- Add a yearly percentage fee, an inflation guess and a target if you want them.
- Read the future value, money paid in, interest, fees and the payment needed for your target.
Future value of an annuity formula
For equal payments at the end of each period, the future value is the payment times ((1 + i)^n - 1) / i. Here i is the rate per payment period and n is the number of payments. For payments at the start of each period (an annuity due), multiply that result by (1 + i).
A starting balance grows on its own, so add P x (1 + i)^n to the payment total. When you add fees or yearly payment changes, the calculator works through every period one at a time instead, so it can track interest, fees and new money separately.
Rate per payment period: i = (1 + r / m)^(m / p) - 1Number of payments: n = years x pOrdinary annuity: FV = PMT x ((1 + i)^n - 1) / iAnnuity due: FV = PMT x ((1 + i)^n - 1) / i x (1 + i)Starting balance: FV = P x (1 + i)^nWhere r = nominal annual rate, m = compounding periods per year, p = payments per year
Example: $10,000 plus $500 a month for 15 years
Start with $10,000 and pay $500 at the end of every month for 15 years. Assume 5% compounded monthly and a 0.50% yearly fee. The projected value is $147,779.10. You paid in $100,000, gross interest adds $53,126.11 and fees take $5,347.01.
With no fee, the same plan reaches $154,781.51, so the fee costs $7,002.41 once lost growth is counted. Against a $200,000 target, you're 73.89% of the way. A starting payment of $703.71 a month would get you there.
| Monthly payment | Money paid in | Future value | Target progress |
|---|---|---|---|
| $500 | $100,000.00 | $147,779.10 | 73.89% |
| $703.71 | $136,667.80 | $199,999.36 | 100.00% after rounding |
| $750 | $145,000.00 | $211,865.62 | 105.93% |
Ordinary annuity vs annuity due
An ordinary annuity pays at the end of each period. An annuity due pays at the start, so each payment gets one extra period of interest (and one extra period of fees). With positive net growth, the annuity due ends higher.
In the example above, switching to start-of-month payments raises the value from $147,779.10 to $148,259.41, a $480.30 difference. Pick the timing that matches when your money goes in.
| Payment timing | Money paid in | Future value | Payment for $200,000 |
|---|---|---|---|
| End of period (ordinary) | $100,000.00 | $147,779.10 | $703.71 |
| Start of period (due) | $100,000.00 | $148,259.41 | $701.09 |
Annuity growth with different rates and fees
The rate drives most of the growth. Keep everything else the same and 4% gives $135,000.63, while 6% gives $162,093.21. That's a gap of more than $27,000 from the same payments.
Fees cut growth twice: once when they're taken, and again because that money stops earning. A 1% yearly fee lowers the example to $141,135.86, costing $13,645.65 against no fee. If a contract's credited rate is already net of fees, set the fee to zero so you don't count it twice.
| Scenario | Gross interest | Future value | Payment for $200,000 |
|---|---|---|---|
| 4% rate, 0.50% fee | $40,032.98 | $135,000.63 | $775.15 |
| 5% rate, 0.50% fee | $53,126.11 | $147,779.10 | $703.71 |
| 6% rate, 0.50% fee | $67,783.10 | $162,093.21 | $636.03 |
Present value of an annuity
Present value runs the same idea backward. It asks what a stream of future payments is worth today at a given rate. The formula is PMT x (1 - (1 + i)^-n) / i.
At 5% compounded monthly, $500 a month for 15 years has a present value of $63,227.62. That's the lump sum you'd need today to fund those payments at that rate. This calculator projects future value only. To see what payments a lump sum can support, use our annuity payout calculator.
Present value (ordinary annuity) = PMT x (1 - (1 + i)^-n) / iPresent value (annuity due) = the line above x (1 + i)
What an annuity contract adds to the math
In finance, an annuity is just a series of regular payments. An insurance annuity is a contract, and its value depends on its terms. Renewal rates, index caps, participation rates, surrender charges, rider costs and bonuses can all make a real contract differ from this smooth projection.
FINRA and the SEC both warn that annuities can carry complex fees and limits on withdrawals. Treat this result as a check on the arithmetic, then compare it line by line with the contract and the insurer's illustration. Taxes, withdrawals and payout options aren't modeled here.
Sources
These public references support the annuity definitions, fee warnings, product types and tax notes used on this page.