What Is an Annuity and How Does It Work?
An annuity is a series of equal, periodic payments made or received at regular intervals over a fixed period. In financial mathematics, annuities model any steady cash flow — mortgage repayments, pension income, savings contributions, and structured settlement payouts. The two quantities an annuity calculator typically solves are the future value (what periodic payments will grow to over time) and the present value (what a stream of future payments is worth in today's money).
The ordinary annuity future value formula is: FV = PMT × [(1 + r)ⁿ − 1] / r, where PMT is the payment per period, r is the periodic interest rate (annual rate divided by payment frequency), and n is the total number of payment periods. The formula was formalised in actuarial mathematics during the 18th century and remains the standard used by financial institutions, pension funds, and loan amortisation schedules worldwide.
For example, a $500 monthly payment invested at a 7% annual rate for 30 years produces a future value of approximately $566,765 — from only $180,000 in contributions, meaning $386,765 (68%) is pure compound interest. The same calculation applies to any currency: £500/month at 5% for 25 years grows to approximately £298,000 in the UK.
Future Value vs Present Value of an Annuity
These two calculations are mirror images of each other, driven by the time value of money — the principle that a payment received today is worth more than the same payment received in the future, because the earlier payment can be invested to earn returns.
| Calculation | Formula | Common Use |
|---|---|---|
| Future Value (FV) | PMT × [(1+r)ⁿ−1] / r | Savings goal, retirement pot |
| Present Value (PV) | PMT × [1−(1+r)^−n] / r | Pension valuation, settlement lump sum |
| Required Payment (PMT) | FV × r / [(1+r)ⁿ−1] | Monthly savings needed for a goal |
Present value calculations are especially important for pension recipients and lottery winners choosing between a lump sum and an annuity payout. According to the U.S. Securities and Exchange Commission, the decision depends heavily on the assumed discount rate: a higher rate makes the lump sum more attractive; a lower rate favours taking the annuity payments.
Ordinary Annuity vs Annuity Due: What Is the Difference?
The timing of payments creates two distinct annuity types. In an ordinary annuity(also called an immediate annuity), payments occur at the end of each period — the standard structure for most loans, mortgages, and pension disbursements. In an annuity due, payments occur at the beginning of each period — common in lease agreements and insurance premiums.
Because annuity due payments are made one period earlier, each payment has an additional compounding period. This makes the future value of an annuity due exactly (1 + r) times greater than an equivalent ordinary annuity. For the $500/month, 7%, 30-year example, the ordinary annuity produces a future value of $566,765 while the annuity due produces approximately $570,079 — a difference of about $3,300 from the timing alone.
How to Use the Annuity Calculator
Select the mode that matches your question, then enter your values — the result updates instantly. Here is what each input means:
- Future Value mode: Enter a regular payment amount (e.g., your monthly savings contribution) to see what it will grow to over time.
- Present Value mode: Enter a regular payment amount (e.g., a pension payout) to find the equivalent lump sum today at a given discount rate.
- Payment mode: Enter a savings goal (future value target) to calculate the regular payment needed to reach it.
- Annual interest rate: Use the expected average return for savings (e.g., 5–8% for a diversified equity portfolio, 3–5% for bonds or fixed annuities).
- Payment frequency: Match the frequency to how often you contribute or receive payments — monthly is most common for savings plans.
This calculator works for any currency. The formulas are identical whether you are working in US dollars, British pounds, euros, Australian dollars, or any other currency. Tax treatment of annuity income varies by country: in the US, annuity payments from a non-qualified annuity are partially taxable; in the UK, annuity income from a pension is subject to income tax in the year it is received; in Australia, superannuation annuities may be tax-free after age 60.
Frequently Asked Questions
What is a good interest rate for an annuity?
Fixed annuity rates from insurance companies typically range from 3% to 6% per year depending on the term and prevailing interest rates. For a savings annuity (regular contributions to an investment account), a long-run real return of 5–7% per year is a commonly used assumption for a diversified global equity portfolio, based on historical data from sources including the Vanguard Global Stock Index. Returns are not guaranteed — use a conservative rate for retirement planning.
How is annuity present value different from future value?
Future value answers "how much will regular payments accumulate to?" while present value answers "how much is a stream of future payments worth right now?" Present value discounts future payments back using the interest rate: a higher discount rate reduces the present value because it implies a stronger preference for money today over money in the future. The two calculations are mathematically inverse — you can solve either from the other given the same payment, rate, and term.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity makes payments at the end of each period (e.g., first mortgage payment due one month after drawdown). An annuity due makes payments at the beginning of each period (e.g., rent paid on the first of the month). The annuity due produces a future value exactly (1 + r) times higher than the equivalent ordinary annuity, because each payment earns one extra compounding period. For most savings plans and investment accounts, the ordinary annuity is the correct model.
How accurate is this annuity calculator?
The calculator uses the standard financial mathematics formulas — the same equations used by actuaries, banks, and financial planning software. Results assume a constant interest rate throughout the term and no fees or taxes. In practice, investment returns fluctuate, and annuity products from insurance companies include profit margins and surrender charges not captured here. Use this calculator for planning estimates, and consult a financial adviser before making significant investment or pension decisions.