Annuity Calculator
An annuity is simply a series of equal payments made at regular intervals — and whether those payments land at the start or the end of each period genuinely changes the final result, even with the identical payment amount and number of periods. This calculator computes future value for both scenarios, letting you see exactly how much that timing difference matters.
How the Annuity Calculator Works
Enter your payment amount per period, the rate per period, the number of periods, and whether payments occur at the beginning or end of each period, and the calculator computes the future value of that entire payment series, along with the present value equivalent, total amount paid in, and total interest earned.
Ordinary Annuity vs. Annuity Due: Why Timing Changes the Math
A payment made at the end of a period (called an “ordinary annuity”) has less time to earn interest before the calculation’s end date than an identical payment made at the beginning of that same period (called an “annuity due”), since the beginning-of-period payment gets one additional period of growth compared to its end-of-period counterpart. This calculator applies a multiplier of (1 + rate) to the standard formula specifically when payments occur at the beginning of each period, correctly reflecting that extra period of compounding — the difference between the two scenarios grows larger with higher rates and more periods, since that extra compounding period compounds itself across the entire series.
Why This Distinction Isn’t Just Academic
Real-world payment timing genuinely varies by context in ways that matter for accurate calculation. Rent and lease payments are typically made at the beginning of each period (an annuity due), since you pay for the period you’re about to occupy, not the one you just finished. Many loan and investment contribution schedules, by contrast, use end-of-period timing (an ordinary annuity) as the more common default convention. Using the wrong timing assumption for your specific real-world scenario — treating an annuity due situation as if it were an ordinary annuity, or the reverse — produces a result that’s subtly but genuinely incorrect, even though the error might not be obvious without directly comparing both calculations side by side.
Present Value and Future Value: Two Sides of the Same Payment Series
This calculator’s future value figure answers “what will this series of payments grow to by the end?” Its companion present value figure answers a related but different question: “what single lump sum today would be exactly equivalent to this entire future payment series?” Both figures describe the identical payment stream, just valued at two different points in time — future value looks forward to the end of the series, present value looks back to a single equivalent amount right now, discounted for the time value of money.
Why Total Interest Earned Can Be a Meaningful Share of the Total
This calculator’s total interest figure — future value minus total payments made — often represents a surprisingly large share of the final total for longer payment series at reasonable rates, precisely because of how compound growth accelerates over many periods. A payment series continued over several decades can see total interest earned meaningfully exceed the sum of all the actual payments contributed, a concrete illustration of why starting a regular contribution habit early, even at a modest amount per period, tends to outperform starting later with larger individual payments over a shorter remaining period.
Retirement Contributions: A Common Real-World Annuity Series
Regular retirement account contributions — a fixed amount deposited every month or every paycheck — are themselves a real-world annuity series, which is exactly why retirement projection calculators use this same underlying future value formula internally. The Retirement Calculator and 401K Calculator apply this identical annuity math specifically to retirement contribution scenarios, with additional retirement-specific framing and goal comparison built on top of the same core calculation.
Converting a Lump Sum Into Payments Instead
This calculator computes the future value building up from a series of regular payments. If you’re working in the opposite direction — starting with an existing lump sum and figuring out what fixed payment it can support over a chosen payout period — the Annuity Payout Calculator handles that reverse calculation, converting an existing balance into a scheduled income stream rather than building one up from contributions.
General Time Value of Money Calculations
This calculator’s payment-series framing is one specific application of the broader time value of money principles used throughout finance. The Finance Calculator provides the full, general five-variable TVM framework (N, I/Y, PV, PMT, FV), which can solve this same type of problem, and several others, with more flexibility than this annuity-specific framing offers.
Comparing Against Simple Compound Growth Without Regular Contributions
If your scenario involves growth on a lump sum with no additional regular contributions, rather than a genuine payment series, that’s a simpler calculation than this annuity calculator addresses. The Compound Interest Calculator covers that more basic case directly, and can also model a hybrid scenario combining an initial lump sum with ongoing contributions together.
Frequently Asked Questions
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity has payments occurring at the end of each period; an annuity due has payments occurring at the beginning of each period. Because beginning-of-period payments have one additional period to earn interest, an annuity due always produces a somewhat higher future value than an ordinary annuity with identical payment amount, rate, and number of periods.
Are rent payments an ordinary annuity or an annuity due?
Typically an annuity due, since rent is generally paid at the beginning of the period you’re about to occupy, not at the end of the period you just completed. Using the correct timing assumption for a specific real-world scenario matters for an accurate calculation.
What is the difference between present value and future value in this context?
Future value is what the entire payment series grows to by the end of the term. Present value is the single lump sum today that would be exactly equivalent to that entire future payment series, discounted for the time value of money. Both describe the same payment stream from two different points in time.
Why can total interest earned exceed total payments made for a long-term annuity?
Because compound growth accelerates over many periods — interest earns interest on itself repeatedly. For sufficiently long payment series at reasonable rates, the cumulative interest earned can genuinely exceed the sum of the actual contributed payments.
Should I use this calculator or the Annuity Payout Calculator?
Use this calculator if you’re building up savings through regular contributions and want to know the resulting future value. Use the Annuity Payout Calculator if you already have a lump sum and want to know what fixed payment it can support over a chosen payout period instead.