Quick answer
Future value of an ordinary annuity FV = P × ((1 + i)ⁿ − 1) ÷ i and present value PV = P × (1 − (1 + i)^−n) ÷ i. Paying $500 monthly at 6% for 10 years accumulates $81,939.67; its present value is $45,036.73, from total payments of $60,000.
Enter the payment, rate, years, frequency and timing. The calculator returns future value, present value and total payments.
Related tools: Lottery Annuity Calculator: Cash value of an annuity-style prize with yearly increases. Annuity Payout Calculator: Monthly payout that exhausts a balance over a set number of years. Present Value of Annuity Calculator: Present value of equal payments at the end of each period.
How to use the Annuity Calculator
- Enter payment each period ($) (above 0).
- Enter annual rate (%) (between 0 and 100).
- Enter years (between 0 and 100).
- Choose payments per year: Monthly, Annually, Semi-annually, Quarterly and Weekly.
- Choose payments: At the end of each period (ordinary) and At the start of each period (due).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Payment each period | A number, in $ | > 0 |
| Annual rate | A number, in % | ≥ 0, ≤ 100 |
| Years | A number | > 0, ≤ 100 |
| Payments per year | Choose one: Monthly; Annually; Semi-annually; Quarterly; Weekly | Starts at Monthly |
| Payments | Choose one: At the end of each period (ordinary); At the start of each period (due) | Starts at At the end of each period (ordinary) |
Formula and method
Formula
FV = P × ((1 + i)ⁿ − 1) ÷ i; PV = P × (1 − (1 + i)^−n) ÷ i (× (1 + i) for annuity due)
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Compounding matches the payment frequency; years × payments per year must be a whole number.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Payment each period = 500; Annual rate = 6; Years = 10; Payments per year = Monthly; Payments = At the end of each period (ordinary).
| Result | Value |
|---|---|
| Future value | $81,939.67 |
| Present value | $45,036.73 |
| Total payments | $60,000.00 |
Example 2
Inputs: Payment each period = 500; Annual rate = 6; Years = 10; Payments per year = Monthly; Payments = At the start of each period (due).
| Result | Value |
|---|---|
| Future value | $82,349.37 |
| Present value | $45,261.91 |
| Total payments | $60,000.00 |
Example 3
Inputs: Payment each period = 1200; Annual rate = 4; Years = 5; Payments per year = Annually; Payments = At the end of each period (ordinary).
| Result | Value |
|---|---|
| Future value | $6,499.59 |
| Present value | $5,342.19 |
| Total payments | $6,000.00 |
The first line is the headline result (future value). Below it the annuity Calculator lists present value and total payments, which describe the same case from other angles. IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice.
Where the growth comes from
You contribute $60,000, so $21,939.67 is interest. Present value is what a stream of payments is worth today at the given rate. For an annuity due (payments at the start of each period) both values are multiplied by (1 + i).
A 0% rate
At a 0% rate, FV is simply payment × number of periods. The rate is nominal annual and compounded at the payment frequency.
How the result changes with payment each period
Holding every other input at the first worked example, this table changes only payment each period. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Payment each period | Future value | Present value | Total payments |
|---|---|---|---|
| 250 | $40,969.84 | $22,518.36 | $30,000.00 |
| 500 | $81,939.67 | $45,036.73 | $60,000.00 |
| 1000 | $163,879.35 | $90,073.45 | $120,000.00 |
| 2000 | $327,758.69 | $180,146.91 | $240,000.00 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Years: entering "2.5" shows "Years × payments per year must be a whole number." beside that field and no result.
- Payment each period: entering "0" shows "Payment each period must be greater than 0." beside that field and no result.
Choosing between the Annuity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Lottery Annuity Calculator](/finance/lottery-annuity/) | total annuity prize, number of yearly payments and yearly increase in payments | Estimated cash value |
| [Annuity Payout Calculator](/finance/annuity-payout-calculator/) | starting balance, annual return and payout period | Monthly payout |
| [Present Value of Annuity Calculator](/finance/present-value-of-annuity/) | payment per period, rate per period and number of periods | Present value |
| [Future Value of Annuity Calculator](/finance/future-value-of-annuity/) | payment per period, rate per period and number of periods | Future value |
| [Auto Loan Calculator](/finance/auto-loan-calculator/) | vehicle price, down payment and interest rate | Monthly payment |
Background: personal finance estimates
Financial calculators project from the numbers you give them. Long-range tools depend on guesses about returns and tax rates that are unlikely to hold exactly, payoff tools assume a fixed payment and rate, and tax or salary results depend on the tax year, filing status and country. Official calculators say their output is for reference only.
For decisions that matter, use conservative inputs and check the figures against your lender, plan documents or a qualified adviser.
Assumptions and limitations
- 0% rate gives payment × periods
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for years and payment each period to confirm this.
Frequently asked questions
What is an ordinary annuity?
One with payments at the end of each period.
What is an annuity due?
One with payments at the start of each period.
Can I use it for a loan?
Yes, PV is the loan amount a payment supports.
What does the Annuity Calculator calculate?
Future and present value of a series of equal payments. It returns Future value, Present value and Total payments.
What formula does the Annuity Calculator use?
FV = P × ((1 + i)ⁿ − 1) ÷ i; PV = P × (1 − (1 + i)^−n) ÷ i (× (1 + i) for annuity due). Compounding matches the payment frequency; years × payments per year must be a whole number.
What do I need to enter in the annuity Calculator?
You enter Payment each period ($), Annual rate (%), Years, Payments per year and Payments.
How is the result rounded or limited?
IEEE-754 double precision; money shown to cents, rates to 4 decimals. Results are estimates, not financial advice. 0% rate gives payment × periods.
What does the “Payments per year” option change?
It sets how the annuity is worked out. The choices are Monthly, Annually, Semi-annually, Quarterly and Weekly.
What is an example of a annuity result?
With payment each period 500, annual rate 6, years 10, payments per year Monthly and payments At the end of each period (ordinary), the future value is $81,939.67.
Can I rely on this calculator for a decision?
Results are estimates for planning, not financial advice. Lender terms, fees, taxes and rounding rules can change real figures, so confirm important numbers with your lender or a licensed adviser. For this calculator in particular: 0% rate gives payment × periods.
Related calculators
- Lottery Annuity Calculator — Cash value of an annuity-style prize with yearly increases.
- Annuity Payout Calculator — Monthly payout that exhausts a balance over a set number of years.
- Present Value of Annuity Calculator — Present value of equal payments at the end of each period.
- Future Value of Annuity Calculator — Future value of equal payments at the end of each period.
- Auto Loan Calculator — Monthly car payment after down payment and trade-in.
- Amortization Calculator — Full amortization schedule with optional extra monthly payments.
- Currency Calculator — Convert an amount using an exchange rate you enter.
Sources
- Standard time-value-of-money relations (e.g. Brealey, Myers & Allen, Principles of Corporate Finance)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.