Annuity Calculator
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Results
$10,000 plus $500.00 a month at 5% compounded monthly grows to $232,643.24 in 20 years
- Initial amount
- $10,000
- Payments
- $120,000
- Interest
- $102,643
| Year | Paid in | Interest | Balance |
|---|---|---|---|
| 1 | $16,000 | $651 | $16,651 |
| 2 | $6,000 | $991 | $23,642 |
| 3 | $6,000 | $1,349 | $30,991 |
| 4 | $6,000 | $1,725 | $38,716 |
| 5 | $6,000 | $2,120 | $46,837 |
| 6 | $6,000 | $2,536 | $55,372 |
| 7 | $6,000 | $2,972 | $64,345 |
| 8 | $6,000 | $3,431 | $73,776 |
| 9 | $6,000 | $3,914 | $83,690 |
| 10 | $6,000 | $4,421 | $94,111 |
The rate is an assumption held steady for the whole term. Annuity contracts can have fees, surrender charges and rates that reset, which are not included here; check the contract.
How to use the annuity calculator
- Enter any initial amount and the payment you will add each period, then choose how often you pay.
- Choose whether payments go in at the start or the end of each period.
- Enter the annual interest rate, how often it compounds and the number of years.
- Read the future value, then open the table to see the balance at the end of every year.
Future value of an annuity formula
r = (1 + i ÷ m)m ÷ p − 1
P is the initial amount, PMT the payment each period, n the number of payments (years × payments per year p) and r the rate per payment period. i is the annual interest rate compounded m times a year. s is 1 when payments are made at the start of each period (an annuity due) and 0 at the end (an ordinary annuity). Paying at the start gives every payment one more period of interest, so the annuity due is worth (1 + r) times as much. This is the same calculation as a spreadsheet's FV function.
Worked examples
Textbook check. $1,000 at the end of each year for 10 years at 5% grows to 1,000 × (1.0510 − 1) ÷ 0.05 = $12,577.89. Paid at the start of each year, it grows to $13,206.79, which is 1.05 times as much.
Monthly payments. $10,000 up front plus $500 at the end of every month for 20 years at 5% compounded monthly gives $232,643.24: $130,000 paid in and $102,643.24 of interest. Making each payment at the start of the month instead gives $233,499.56, $856.32 more.
Future value of $100 a month
Payments at the end of each month, monthly compounding, no initial amount.
| Rate | 10 years | 20 years | 30 years |
|---|---|---|---|
| 3% | $13,974.14 | $32,830.20 | $58,273.69 |
| 4% | $14,724.98 | $36,677.46 | $69,404.94 |
| 5% | $15,528.23 | $41,103.37 | $83,225.86 |
| 6% | $16,387.93 | $46,204.09 | $100,451.50 |
| 7% | $17,308.48 | $52,092.67 | $121,997.10 |
Over 30 years you pay in $36,000 in every row; the rest is interest. At 7% the interest is about 2.4 times what you paid in.
Using the result well
- Annuity maths vs annuity products. In finance, an annuity is any series of equal payments, such as savings deposits. An insurance annuity contract adds fees, surrender charges and rules for withdrawals, so read the contract before comparing it with this figure.
- Fixed rates may not last. Many fixed annuities guarantee a rate for a few years, then reset. Try a lower rate for the later years to see the effect.
- Taxes. Growth inside a deferred annuity is usually tax-deferred, but earnings are taxed as income when withdrawn and early withdrawals can be penalized.
- Turning it into income. When the money is built up, the annuity payout calculator shows the income it can pay. For returns that vary, use the investment calculator; for a single sum, the future value calculator.
Frequently asked questions
How do you calculate the future value of an annuity?
Multiply the payment by [(1 + r)^n − 1] ÷ r, where r is the rate per period and n the number of payments, and add the growth on any initial amount. $1,000 at the end of each year for 10 years at 5% grows to 1,000 × (1.05^10 − 1) ÷ 0.05 = $12,577.89.
What is the difference between an annuity due and an ordinary annuity?
An ordinary annuity pays at the end of each period; an annuity due pays at the start, so each payment earns one extra period of interest. The 10-year example above is worth $13,206.79 as an annuity due, exactly 1.05 times the ordinary annuity.
How much will $500 a month grow to in 20 years?
At an assumed 5% compounded monthly, with $10,000 to start and $500 at the end of each month, it grows to about $232,643.24. You pay in $130,000, and the rest, $102,643.24, is interest.
Does the compounding frequency matter?
A little. $100 a month for 30 years at 5% grows to $81,537.59 with yearly compounding, $83,225.86 with monthly compounding and $83,386.57 with continuous compounding. Use the compounding your account or contract states.
Does this include annuity fees and taxes?
No. The calculator shows the maths of a series of payments at a steady rate. Annuity contracts can charge fees and surrender charges, and their earnings are usually taxed as income when withdrawn, so check the contract and your tax situation.