Annuity Calculator: Future Value and Present Value
This annuity calculator finds the future value and present value of a series of equal payments, for an ordinary annuity (paid at the end of each period) or an annuity due (paid at the start). It runs privately in your browser.
An annuity calculator works out what a series of equal, regularly spaced payments is worth. Future value is the balance those payments grow to at a given interest rate. Present value is the single sum today that equals the same payments. Both depend on the payment, the rate, the number of periods and payment timing.
How the Annuity Calculator Works
Enter the payment per period, the annual interest rate, the number of years, how often payments are made, and whether each payment falls at the end or the start of its period. The calculator then:
- Converts the rate. Rate per period r = annual rate ÷ payments per year. A 6% rate with monthly payments is 0.5% a month.
- Counts the payments. n = years × payments per year.
- Applies the ordinary annuity formulas below for future value and present value.
- Adjusts for an annuity due. If payments are made at the start of each period, both values are multiplied by (1 + r), because every payment earns one extra period of interest.
- Reports the effective annual rate, (1 + r)m − 1, where m is payments per year. Interest is compounded once per payment period.
Formulas
FV (ordinary) = PMT × ((1 + r)^n - 1) / r
PV (ordinary) = PMT × (1 - (1 + r)^(-n)) / r
Annuity due = ordinary result × (1 + r)
Where PMT = payment per period, r = interest rate per period, n = total number of periods.
Annuity Formula: Worked Example
Take $500 a month for 20 years at 6% a year. That is r = 0.5% per month and n = 240 payments. Entering those numbers above gives these results for each payment timing.
| Result | Ordinary annuity (end of month) | Annuity due (start of month) |
|---|---|---|
| Future value | $231,020.45 | $232,175.55 |
| Present value | $69,790.39 | $70,139.34 |
| Total payments | $120,000.00 | $120,000.00 |
| Interest earned | $111,020.45 | $112,175.55 |
| Effective annual rate | 6.17% | 6.17% |
Paying at the start of each month adds $1,155.10 to the future value. That is exactly 0.5% more, because each of the 240 payments stays invested one month longer.
Ordinary Annuity vs Annuity Due
The only difference between the two is when each payment is made, but it changes every result.
| Ordinary annuity | Annuity due | |
|---|---|---|
| Payment falls | End of each period | Start of each period |
| Typical examples | Loan repayments, bond coupons | Rent, insurance premiums, lease payments |
| Future value | PMT × ((1 + r)^n - 1) / r | Ordinary FV × (1 + r) |
| Present value | PMT × (1 - (1 + r)^(-n)) / r | Ordinary PV × (1 + r) |
| Which is larger? | Smaller | Larger by a factor of (1 + r) |
Future Value vs Present Value of Annuity
The future value of an annuity answers the question: "If I invest a fixed amount each period, how much will I have at the end?" This is useful for planning retirement savings or education funds. The present value of an annuity answers: "What is a stream of future payments worth today?" This is useful for evaluating pension buyouts, structured settlements, or determining the fair price of an income-producing investment.
Both calculations assume a constant interest rate and equal payments. In practice, interest rates change and some annuity products pay variable returns, so treat the result as a baseline projection.
Annuity Math vs Annuity Products
This page does the time-value-of-money math for any stream of equal payments. An annuity sold by an insurance company is a contract, and its value also depends on fees, surrender charges and payout options.
- Fixed annuity: pays a rate set in the contract. To estimate the income a lump sum can provide, use the annuity payout calculator.
- Variable annuity: returns depend on the underlying investments, and annual fees reduce them. The variable annuity fee impact calculator shows what those fees cost over time.
Practical Applications
Annuity calculations sit behind many financial decisions. Use them to see what a monthly saving habit grows to, to judge whether a lump sum or a series of payments is the better pension offer, or to compare savings plans with different payments and interest rates. Because of the time value of money, starting earlier with smaller payments often beats larger payments started later.
Last updated: October 2026
Frequently Asked Questions
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity makes payments at the end of each period, like most loan repayments. An annuity due makes payments at the beginning of each period, like rent. This calculator does both: choose the payment timing and it shows the future value and present value for that type. An annuity due is worth (1 + r) times the ordinary annuity, where r is the rate per period.
How does payment frequency affect the future value?
More frequent payments give a higher future value, because each payment starts earning interest sooner and interest compounds more often. At 6% a year for 20 years, $6,000 paid once a year grows to $220,713.55, while $500 paid monthly grows to $231,020.45.
What is present value of an annuity used for?
Present value tells you what a future stream of payments is worth today. It is used to evaluate pension lump-sum offers, determine fair prices for structured settlements, compare investment alternatives, and assess whether it is better to take a lump sum now or receive payments over time.
Can I use this for retirement planning?
Yes. Enter your planned contribution, the annual return you expect and the years until retirement. The future value is your projected balance. It assumes a constant rate and equal payments, and it does not allow for inflation, taxes, fees or changing market returns.
What interest rate should I use?
Use the rate that fits the money. For a savings account or certificate of deposit, use the APY on offer. For a fixed annuity or a loan, use the contract rate. For long-term investments no rate is guaranteed, so run a lower and a higher rate to see the range of outcomes.
What is the formula for the future value of an annuity?
For an ordinary annuity, FV = PMT x ((1 + r)^n - 1) / r, where PMT is the payment per period, r is the interest rate per period and n is the number of payments. For an annuity due, multiply the result by (1 + r). Example: $500 a month at 6% a year for 20 years gives a future value of $231,020.45.
How much does a $100,000 annuity pay per month?
It depends on the rate and the term. As a fixed-period calculation, $100,000 paid out over 20 years at 5% a year supports about $659.96 a month: enter that payment here and the present value comes back as roughly $100,000. Lifetime payouts from an insurer also depend on your age and the contract, so treat this as math, not a quote.