Retirement
How To Calculate Annuity Future Value
An annuity is a series of equal payments made at regular intervals, such as a monthly contribution into a retirement account or a monthly withdrawal from it. The future value tells you what the whole stream grows to by the end of the term, the present value tells you what that stream is worth in today's money, and the gap between them is the effect of compounding.
Quick Answer
FV = PMT x ((1 + i)^n - 1) / i
- PMT
- Payment made each period
- i
- Interest rate per period
- n
- Number of periods
Five hundred dollars a month for twenty years at six percent a year grows to about 231,020 dollars. You paid in 120,000 dollars, so roughly 111,020 dollars of the final balance is interest rather than contributions.
What Is Annuity Future Value?
An annuity is a series of equal payments made at regular intervals, such as a monthly contribution into a retirement account, a monthly pension payout, or a fixed instalment on a lease. The payments are level, the gaps between them are equal, and the rate is assumed to stay the same throughout the term.
Two figures matter most. The future value is what the whole stream grows to by the end of the term. The present value is what that same stream is worth today, once every future payment has been discounted back at the same rate.
The future value formula takes each payment, compounds it forward to the final date, and adds the results together. Because the payments are equal and equally spaced, the sum collapses into a single expression: the payment times an annuity factor, which is one plus the periodic rate raised to the number of periods, minus one, all divided by the periodic rate.
The present value formula works in the opposite direction. Each payment is discounted back to today, and the sum again collapses into one expression. The two values are linked: the present value multiplied by one plus the periodic rate raised to the number of periods gives the future value.
The periodic rate and the number of periods must match the payment frequency. A six percent annual rate paid monthly is half a percent per month, and twenty years of monthly payments is two hundred and forty periods. Mixing an annual rate with a monthly period count overstates the result badly.
Payments can fall at the end of each period or at the beginning. An ordinary annuity pays at the end, which is the usual convention for deposit and loan streams. An annuity due pays at the start, so every payment earns one extra period of interest, and both the future value and the present value are larger by a factor of one plus the periodic rate.
The total paid in is simply the payment multiplied by the number of periods. The interest earned is the future value minus that total. Early in the term almost all of the balance is contributions; later, interest dominates, which is why the final years of a long annuity can add more than the first decade.
Compounding is what separates the future value from the sum of the payments. At a high rate over a long term the gap is enormous, and it is the reason the interest figure rather than the deposit figure is the headline result in most retirement projections.
An annuity with no end date is a perpetuity, whose present value is the payment divided by the periodic rate. Finite annuities converge towards that limit as the term lengthens, which is a useful sanity check on a long-dated calculation.
The same mathematics runs a loan in reverse. A mortgage payment is the payment on an annuity whose present value is the loan amount, so the payment formula is the present value formula solved for the payment rather than for the value.
Lottery payouts, structured settlements and pension buyouts are all annuities in disguise. Comparing a lump sum against a stream of payments is a present value calculation, and the answer depends heavily on the discount rate chosen.
Inflation is not in the formula. A future value expressed in nominal dollars buys less than the same figure today, so a real return, meaning the nominal rate minus expected inflation, is the better input when the goal is purchasing power rather than a headline balance.
The calculator assumes level payments, a constant rate, and no fees or taxes. Real accounts carry expense ratios, contribution limits and tax treatment that change the arithmetic, so treat the output as the mathematical baseline rather than a forecast.
Formula
FV = PMT x ((1 + i)^n - 1) / i
Each payment is compounded to the end of the term and the results are added.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| PMT | Payment per period | currency | The equal payment made at each interval. |
| i | Rate per period | decimal | Annual rate divided by the number of payments a year. |
| n | Number of periods | count | Years multiplied by the payments per year. |
PV = PMT x (1 - (1 + i)^-n) / i
Each payment is discounted back to today and the results are added.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| PMT | Payment per period | currency | The equal payment made at each interval. |
| i | Rate per period | decimal | Annual rate divided by the number of payments a year. |
| n | Number of periods | count | Years multiplied by the payments per year. |
How To Calculate Annuity Future Value
- 1
Match the rate to the payment frequency
Divide the annual rate by the number of payments a year. Six percent a year paid monthly is half a percent a month.
- 2
Count the periods
Multiply the number of years by the payments per year. Twenty years of monthly payments is two hundred and forty periods.
- 3
Build the annuity factor
Raise one plus the periodic rate to the number of periods, subtract one, and divide by the periodic rate.
- 4
Multiply by the payment
The annuity factor times the payment gives the future value of an ordinary annuity. Multiply by one plus the periodic rate for an annuity due.
- 5
Split the result
The payment times the number of periods is the total paid in. The future value minus that total is the interest earned.
Examples
Example 1: 500 a month for 20 years at 6 percent
- Payment amount
- 500
- Annual interest rate
- 6
- Years
- 20
- Payments per year
- Monthly
- Payment timing
- End of period (ordinary)
| Step | Calculation | Result |
|---|---|---|
| Periods | 20 x 12 | 240 |
| Rate per period | 6 / 12 | 0.5 |
| Growth factor | 1.005 ^ 240 | 3.310204 |
| Future value | 500 x ((3.310204 - 1) / 0.005) | 231020.45 |
| Total paid in | 500 x 240 | 120000.00 |
| Interest earned | 231020.45 - 120000.00 | 111020.45 |
Result: The stream grows to 231,020.45 by the end of twenty years. You paid in 120,000.00, so 111,020.45 of the balance is interest.
Example 2: 500 a year for 20 years at 6 percent
- Payment amount
- 500
- Annual interest rate
- 6
- Years
- 20
- Payments per year
- Annual
- Payment timing
- End of period (ordinary)
| Step | Calculation | Result |
|---|---|---|
| Periods | 20 x 1 | 20 |
| Rate per period | 6 / 1 | 6 |
| Growth factor | 1.06 ^ 20 | 3.207135 |
| Future value | 500 x ((3.207135 - 1) / 0.06) | 18392.80 |
| Total paid in | 500 x 20 | 10000.00 |
| Interest earned | 18392.80 - 10000.00 | 8392.80 |
Result: One payment a year of 500 grows to 18,392.80 over twenty years. The 10,000.00 paid in leaves 8,392.80 of interest.
Calculator
Future value
$231,020.45
- Present value
- $69,790.39
- Total paid in
- $120,000.00
- Interest earned
- $111,020.45
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the Annuity Future Value calculator page.
Common Mistakes
Mixing an annual rate with monthly periods
Using six as the rate and two hundred and forty as the count gives a number many times too large. Divide the rate by the same frequency you multiply the years by.
Forgetting that payments can fall at the start
An annuity due earns one extra period of interest on every payment. Leaving the timing at the default when payments actually arrive at the beginning understates the result.
Treating the future value as profit
The future value includes your own contributions. Only the future value minus the total paid in is interest, and that is the figure worth comparing across options.
Ignoring fees and taxes
Expense ratios and tax are charged against the balance and quietly reduce the effective rate. A fund charging one percent a year on a six percent return gives up a sixth of the growth.
Assuming the rate holds for decades
Rates change. A single fixed rate over twenty or thirty years is a simplifying assumption, so a range of rates is more honest than one number.
Overlooking inflation
A future value in nominal dollars is not the same as purchasing power. Subtract expected inflation to see what the balance will actually buy.
Rounding the periodic rate too early
Rounding six percent divided by twelve to a whole number destroys the result. Keep the periodic rate at full precision until the final step.
FAQ
What is the difference between future value and present value?
The future value is what the stream grows to at the end of the term; the present value is what that same stream is worth today. The present value times one plus the periodic rate raised to the number of periods gives the future value.
What is an ordinary annuity versus an annuity due?
An ordinary annuity pays at the end of each period and an annuity due pays at the beginning. Because every due payment earns one extra period of interest, the annuity due is larger by a factor of one plus the periodic rate.
How do I pick the periodic rate?
Divide the annual rate by the number of payments per year. Six percent a year paid monthly is half a percent per month, and the period count must use the same frequency.
Why is the interest so large on a long annuity?
Compounding. Each payment earns interest for the rest of the term, so the earliest payments do most of the work and the balance accelerates as the term lengthens.
Can the calculator handle a zero percent rate?
Yes. At a zero rate the future value is simply the payment multiplied by the number of periods, since there is no interest to compound and the expression falls back to that figure.
Does the calculator include inflation or fees?
No. It models level payments at a constant nominal rate with no costs. For a real-terms answer, enter the rate net of inflation and fees.
References
- [1]Investopedia, Future Value of an Annuity — https://www.investopedia.com/terms/f/future-value-annuity.asp
- [2]Investopedia, Present Value of an Annuity — https://www.investopedia.com/terms/p/present-value-annuity.asp
- [3]U.S. Securities and Exchange Commission, Compound Interest Calculator — https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator