People type this into search every day: annuity calculator.
On this page an annuity is a string of equal deposits. Each deposit earns compound interest until the end date. Investor.gov’s future value glossary calls future value the worth of an asset on a later date. Their compound interest glossary is the engine underneath: interest on principal and on interest already earned.
The future value of an annuity calculator uses the ordinary-annuity formula, plus a switch when the deposit lands at the start of the period:
Ordinary FV = payment × ((1 + r)^n − 1) ÷ r
Annuity due = ordinary FV × (1 + r)
r is the annual rate divided by the number of deposits in a year. n is the years times that same count. When the rate is zero, the future value is payment times n, so the formula does not divide by zero.
Fees, taxes, and a starting lump sum stay out. Money that is already in the account belongs on the compound savings calculator. One future sum, discounted back, belongs on the present value calculator. The present value post walks that single-sum case.
These are labeled examples. An insurance annuity, with fees and surrender rules, is a different contract. This page is not personalized financial advice.
Fig 1
Equal deposits, then interest
The periodic rate is the annual rate split by the deposits in a year
End-of-period deposits use the ordinary formula. Start-of-period deposits multiply that result by one plus the periodic rate.
Example 1. Five hundred dollars at the end of each month
This is the calculator’s published example.
- Deposit each period: $500
- Annual rate: 5%
- Years: 10
- Deposits per year: 12
- Timing: end of each period
The periodic rate is 0.05 ÷ 12. The deposit count is 10 × 12 = 120.
Future value = 500 × ((1 + 0.05/12)^120 − 1) ÷ (0.05/12).
That periodic rate is a repeating decimal, so a rounded hand calculation can miss a penny. The calculator evaluates the full expression and prints $77,641.14.
Cash deposited is 500 × 120 = $60,000.00.
Interest is 77,641.14 − 60,000.00 = $17,641.14.
Calculator result
Future value of an annuity
- Deposit each period
- $500.00
- Annual interest rate
- 5%
- Years
- 10 years
- Deposits per year
- 12
- When each deposit lands
- 0
$77,641.14
ordinary-annuity future value
- Total deposited
- $60,000.00
- Interest earned
- $17,641.14
- Number of deposits
- 120
Fig 2 · 1/2
Where $77,641.14 comes from
$500 at the end of each month, 5%, 10 years
Deposited
$60,000.00
Interest
$17,641.14
The 120 deposits add up to $60,000.00.
Interest is $17,641.14, which is 22.7% of the ending balance.
Interest’s share is 17,641.14 ÷ 77,641.14 = 22.7%. The deposits are the other 77.3%. Ten years of monthly saving, at this rate, is still mostly the cash you put in.
Example 2. The same deposit at 3 percent and at 7 percent
Hold $500 a month, 10 years, and end-of-month timing. Change only the annual rate.
At 3% the future value is $69,870.71. Interest is 69,870.71 − 60,000.00 = $9,870.71.
At 5% you are back on example 1: $77,641.14, and $17,641.14 of interest.
At 7% the future value is $86,542.40. Interest is 86,542.40 − 60,000.00 = $26,542.40.
Calculator result
Future value of an annuity
- Annual interest rate
- 7%
$86,542.40
ordinary-annuity future value
- Total deposited
- $60,000.00
- Interest earned
- $26,542.40
- Number of deposits
- 120
The step from 5% to 7% adds 86,542.40 − 77,641.14 = $8,901.26 on the same $60,000. The step from 3% to 5% adds 77,641.14 − 69,870.71 = $7,770.43.
Fig 3 · 1/3
Ten-year balance at three rates
$500 at each month-end. Only the annual rate changes.
- Future value
| Category | Future value |
|---|---|
| 3% | $70k |
| 5% | $78k |
| 7% | $87k |
At 3% the balance is $69,870.71.
At 5% it is $77,641.14. At 7% it is $86,542.40.
A higher rate does more in the later years. Example 4 puts the same 5% and 7% rates on a 30-year span, and the gap is no longer a few thousand dollars.
Example 3. What if the monthly deposit changes?
The formula is linear in the payment when the rate, the years, and the timing stay put. Double the deposit and every output doubles.
Keep 5%, 10 years, monthly, end of period.
- $250 a month: future value $38,820.57. Deposited $30,000.00. Interest $8,820.57.
- $500 a month: $77,641.14, $60,000.00, $17,641.14.
- $1,000 a month: $155,282.28, $120,000.00, $35,282.28.
The check is arithmetic. 77,641.14 × 2 = 155,282.28. And 77,641.14 ÷ 2 = 38,820.57.
If your plan is “save twice as much,” you do not need a new rate assumption to see the new balance. You scale example 1. The rate and the years are what bend the interest line.
Example 4. What if the time span changes?
Hold $500, a 5% annual rate, monthly deposits, end of period. Change the years.
- 5 years: 60 deposits, $30,000.00 in, future value $34,003.04, interest $4,003.04.
- 10 years: $60,000.00 in, $77,641.14, interest $17,641.14.
- 15 years: $90,000.00 in, $133,644.47, interest $43,644.47.
- 20 years: $120,000.00 in, $205,516.83, interest $85,516.83.
- 25 years: $150,000.00 in, $297,754.85, interest $147,754.85.
- 26 years: $156,000.00 in, $319,127.99, interest $163,127.99.
- 30 years: $180,000.00 in, $416,129.32, interest $236,129.32.
Calculator result
Future value of an annuity
- Years
- 30 years
$416,129.32
ordinary-annuity future value
- Total deposited
- $180,000.00
- Interest earned
- $236,129.32
- Number of deposits
- 360
At 25 years, interest is still short of the cash deposited: 150,000.00 − 147,754.85 = $2,245.15. At 26 years, interest moves ahead: 163,127.99 − 156,000.00 = $7,127.99. By year 30, interest is 236,129.32 − 180,000.00 = $56,129.32 ahead of the deposits. That interest is 236,129.32 ÷ 416,129.32 = 56.7% of the ending balance.
Fig 4 · 1/7
Balance every five years
$500 at month-end, 5% annual rate, ordinary annuity
Future value
- Balance
| Point | Balance |
|---|---|
| 0y | $0.00 |
| 5y | $34k |
| 10y | $78k |
| 15y | $134k |
| 20y | $206k |
| 25y | $298k |
| 30y | $416k |
After 10 years the balance is $77,641.14.
After 30 years it is $416,129.32, and interest is more than the cash deposited.
Fig 5 · 1/2
Deposits and interest
Same $500 monthly deposit at 5%
- Deposited
- Interest
| Category | Deposited | Interest |
|---|---|---|
| 5 years | $30k | $4.0k |
| 10 years | $60k | $18k |
| 20 years | $120k | $86k |
| 30 years | $180k | $236k |
Deposits are $30,000, $60,000, $120,000, and $180,000.
Interest is $4,003.04, $17,641.14, $85,516.83, and $236,129.32.
The Rule of 72 post estimates how long one lump sum takes to double. That shortcut does not date an annuity, because new money keeps arriving. On this $500 stream at 5%, the balance first exceeds twice the cash deposited during year 26.
The same deposits at 7% grow faster, and the gap versus 5% widens with time.
- 10 years at 7%: $86,542.40
- 20 years at 7%: $260,463.33, interest $140,463.33 on $120,000 deposited
- 30 years at 7%: $609,985.50, interest $429,985.50 on $180,000 deposited
Fig 6 · 1/2
Five percent against seven percent
$500 at each month-end
- 5% rate
- 7% rate
| Category | 5% rate | 7% rate |
|---|---|---|
| 10 years | $78k | $87k |
| 20 years | $206k | $260k |
| 30 years | $416k | $610k |
At 5% the balances are $77,641.14, $205,516.83, and $416,129.32.
At 7% they are $86,542.40, $260,463.33, and $609,985.50.
At 30 years the 7% balance is 609,985.50 − 416,129.32 = $193,856.18 higher, on the same $180,000 of deposits. At 10 years that rate gap was $8,901.26.
Example 5. Monthly, quarterly, or once a year
Put the same $60,000 in over 10 years at 5%, at the end of each period. Only the spacing changes.
- Once a year, $6,000: 10 deposits. Future value $75,467.36. Interest $15,467.36.
- Each quarter, $1,500: 40 deposits. Future value $77,234.34. Interest $17,234.34.
- Each month, $500: 120 deposits. Future value $77,641.14. Interest $17,641.14.
Monthly beats the annual deposit by 77,641.14 − 75,467.36 = $2,173.78. Monthly beats quarterly by 77,641.14 − 77,234.34 = $406.80.
The cash total matches. The earlier deposits in the monthly plan get more periods of interest, so the ending balance is higher. The quarterly plan sits close to the monthly one. Most of the extra interest, versus writing one check a year, shows up as soon as you split the year into four.
A related slip is to leave the payment at $500 and switch the frequency to annual. That story is $500 a year, not $500 a month. Ten annual deposits of $500 grow to $6,288.95. Cash in is $5,000.00. Interest is $1,288.95. Next to the monthly result of $77,641.14, the frequency box and the payment box have to describe the same habit.
Example 6. Deposit at the start of the month
Same $500, 5%, 10 years, monthly. Move each deposit to the start of the period. That is the annuity-due case. The formula multiplies the ordinary result by (1 + r), and r is still 0.05 ÷ 12.
The calculator prints $77,964.64.
Deposits are still $60,000.00. Interest is 77,964.64 − 60,000.00 = $17,964.64.
The gap versus example 1 is 77,964.64 − 77,641.14 = $323.50. Each of the 120 deposits earns one extra month.
A shorter case, so the gap is not only a ten-year story: $200 a month, 4%, 15 years, 180 deposits, $36,000.00 deposited.
- End of the month: future value $49,218.10. Interest $13,218.10.
- Start of the month: future value $49,382.16. Interest $13,382.16.
The due switch adds 49,382.16 − 49,218.10 = $164.06.
Example 7. A zero rate, and a short low rate
Set the rate to 0% on the example 1 deposits. Future value equals payment × n.
500 × 120 = $60,000.00. Interest is $0.00.
A short, low-rate stretch stays close to the cash too. $50 a month, 2%, 3 years, end of month:
- Deposits: 50 × 36 = $1,800.00
- Future value: $1,853.51
- Interest: 1,853.51 − 1,800.00 = $53.51
Three years at 2% adds $53.51. The 30-year row in example 4 is where the interest line gets large. A short window will not show that, even when the formula is the same one.
Example 8. The lump-sum mistake
A common slip is to add the deposits first, then compound the total as one lump sum that was there on day one.
Cash in over 10 years at $500 a month is $60,000. Compound that whole pile for 10 years at 5%, once a year:
60,000 × 1.05^10 = $97,733.68
Investor.gov’s classroom page grows $100 at 5% for 10 years, and the compound interest post writes that as 100 × 1.05^10 = $162.89. Scaling the rounded $162.89 by 600 lands a penny away from $97,733.68. Run the power on $60,000 itself.
The annuity result for the same cash, dripped in at month-end, is $77,641.14.
The lump-sum figure is 97,733.68 − 77,641.14 = $20,092.54 higher. It pretends the last deposits had ten years to earn, when some of them had a month.
Example 9. One hundred dollars a month for thirty years
- Deposit: $100
- Annual rate: 6%
- Years: 30
- Deposits per year: 12
- Timing: end of each period
Deposit count: 30 × 12 = 360.
Cash in: 100 × 360 = $36,000.00.
Future value: $100,451.50.
Interest: 100,451.50 − 36,000.00 = $64,451.50.
Interest is larger than the cash deposited. Its share of the ending balance is 64,451.50 ÷ 100,451.50 = 64.2%.
Set this next to example 7. The same formula, at 2% for 3 years, added $53.51. At 6% for 30 years, interest is $64,451.50 on $36,000 of deposits. The rate and the deposit count do that work. The payment size, as example 3 showed, only scales it.
Nine annuities side by side
Every row uses the calculator formula. Timing is the end of the period unless the row says start.
| Example | Payment | Rate | Years | How often | Deposited | Future value | Interest |
|---|---|---|---|---|---|---|---|
| 1. Published case | $500 | 5% | 10 | Monthly | $60,000.00 | $77,641.14 | $17,641.14 |
| 2. Lower rate | $500 | 3% | 10 | Monthly | $60,000.00 | $69,870.71 | $9,870.71 |
| 2. Higher rate | $500 | 7% | 10 | Monthly | $60,000.00 | $86,542.40 | $26,542.40 |
| 3. Smaller deposit | $250 | 5% | 10 | Monthly | $30,000.00 | $38,820.57 | $8,820.57 |
| 3. Larger deposit | $1,000 | 5% | 10 | Monthly | $120,000.00 | $155,282.28 | $35,282.28 |
| 4. Short horizon | $500 | 5% | 5 | Monthly | $30,000.00 | $34,003.04 | $4,003.04 |
| 4. Long horizon | $500 | 5% | 30 | Monthly | $180,000.00 | $416,129.32 | $236,129.32 |
| 4. Long horizon, 7% | $500 | 7% | 30 | Monthly | $180,000.00 | $609,985.50 | $429,985.50 |
| 5. Annual check | $6,000 | 5% | 10 | Yearly | $60,000.00 | $75,467.36 | $15,467.36 |
| 5. Quarterly | $1,500 | 5% | 10 | Quarterly | $60,000.00 | $77,234.34 | $17,234.34 |
| 6. Start of month | $500 | 5% | 10 | Monthly, due | $60,000.00 | $77,964.64 | $17,964.64 |
| 7. Zero rate | $500 | 0% | 10 | Monthly | $60,000.00 | $60,000.00 | $0.00 |
| 7. Short and low | $50 | 2% | 3 | Monthly | $1,800.00 | $1,853.51 | $53.51 |
| 8. Lump-sum slip | $60,000 on day one | 5% | 10 | One sum | $60,000.00 | $97,733.68 | $37,733.68 |
| 9. Small and long | $100 | 6% | 30 | Monthly | $36,000.00 | $100,451.50 | $64,451.50 |
Example 8 is the mistake row. It compounds $60,000 × 1.05^10. Interest on that row is 97,733.68 − 60,000.00 = $37,733.68, and the balance is $20,092.54 above the real monthly annuity.
The rate you type is an assumption you chose. The calculator does not know the fee, the tax, or whether the rate stays at that number. Open the annuity calculator with your deposit, your rate, and your years. A balance you already hold goes to the compound savings calculator. One amount on a future date goes to the present value calculator.