What Is an Annuity?
An annuity is a financial arrangement involving a series of equal payments made at regular intervals. While insurance companies sell annuity contracts that guarantee lifetime income, the underlying math applies to any situation involving regular cash flows — retirement drawdowns, savings accumulation plans, structured settlements, and mortgage payments all use annuity formulas at their core.
This calculator covers three distinct annuity problems. The first asks: given a nest egg, how much can I withdraw each month without running out? The second asks: if I save a fixed amount each month, how much will I have at a future date? The third asks: what lump sum do I need today to fund a specific monthly payment for a set number of years?
All three calculations use the same underlying time-value-of-money framework — the idea that a dollar today is worth more than a dollar in the future because today's dollar can be invested and earn returns.
The Three Calculation Modes Explained
Mode 1: Monthly Payment from Lump Sum
This is the classic retirement drawdown scenario. You have a nest egg — say, $500,000 — and you want to know how much you can withdraw each month for exactly 20 years before the balance reaches zero. The formula accounts for the interest your remaining balance continues to earn throughout the drawdown period.
The formula for an ordinary annuity payment is:
PMT = PV × r / [1 − (1 + r)^(−n)]
Where PV is the present value (lump sum), r is the monthly interest rate (annual rate ÷ 12), and n is the total number of months. A $500,000 nest egg earning 5% annually for 20 years can support a monthly withdrawal of approximately $3,300.
Mode 2: Future Value from Payments
This mode answers the saving question: if you invest $500 per month for 30 years at a 7% annual return, what will your account be worth? The future value formula compounds each payment from the date it is made to the end of the investment horizon.
FV = PMT × [(1 + r)^n − 1] / r
This is the engine behind 401(k) projections. Regular contributions, even modest ones, can grow dramatically over long periods thanks to compounding. Monthly contributions of $500 at 7% for 30 years produce a future value of over $566,000 — from only $180,000 of actual deposits.
Mode 3: Present Value from Payments
This mode asks: what single lump sum, invested today at a given rate, would fund a specific monthly payment for a set number of years? This is useful for evaluating pension buyouts, structured settlements, or planning how much to accumulate before retirement to support a target income.
PV = PMT × [1 − (1 + r)^(−n)] / r
If you want $2,500 per month for 25 years and expect to earn 5% annually, you need approximately $425,000 as a lump sum today. Knowing this target helps you work backward to determine your required savings rate during your working years.
Ordinary Annuity vs. Annuity-Due
The timing of payments within each period creates two distinct annuity types. In an ordinary annuity, payments occur at the end of each period. This is the standard assumption for most loans, mortgage payments, and retirement drawdowns. In an annuity-due, payments occur at the beginning of each period — like rent, which is typically paid at the start of the month rather than the end.
The difference is subtle but meaningful. Because annuity-due payments arrive one period earlier, each payment has an extra period of compounding time. For an accumulation scenario, this produces a slightly higher future value. For a drawdown or present value scenario, annuity-due payments require a slightly larger lump sum (or allow a slightly smaller monthly withdrawal for the same balance).
The adjustment is simple: multiply the ordinary annuity result by (1 + r), where r is the monthly rate. For most practical planning purposes, the difference between ordinary and annuity-due is small — under 0.5% at typical interest rates — but it matters for precise contract valuations.
A Practical Example
Suppose you are 60 years old and plan to retire at 65 with $600,000 in savings. You expect your portfolio to earn 5% annually in retirement and want the money to last 25 years (until age 90). Using Mode 1:
- Lump sum: $600,000
- Annual rate: 5%
- Years: 25
- Annuity type: Ordinary
The result is a monthly payment of approximately $3,511. Over 25 years you would withdraw $1,053,300 — $453,300 more than your original $600,000 — because the remaining balance continues to earn interest throughout the drawdown period.
If you wanted $4,000 per month instead, you could flip to Mode 3 to find that you would need approximately $683,000 as a starting balance — giving you a concrete savings target to work toward before retirement.
Questions You Might Ask
What is an annuity?
An annuity is a series of equal payments made at regular intervals over a fixed period. In personal finance, annuities most commonly refer to retirement income arrangements — either a drawdown from a nest egg or a savings plan that accumulates through regular contributions. Insurance companies also sell annuity contracts that guarantee lifetime income in exchange for a lump-sum premium.
What is the difference between an ordinary annuity and an annuity-due?
In an ordinary annuity, payments occur at the end of each period — the default assumption for most loans and retirement drawdowns. In an annuity-due, payments occur at the beginning of each period, like rent. Annuity-due produces a slightly higher future value or requires a slightly larger present value than an otherwise identical ordinary annuity.
How do I calculate how long my retirement savings will last?
Use Mode 1 (Monthly Payment from Lump Sum). Enter your nest egg, expected return rate, and the number of years you want the money to last. The calculator finds the maximum monthly withdrawal that draws the balance to exactly zero at the end of your chosen period.
What is the present value of an annuity?
The present value of an annuity is the lump sum needed today, invested at a given rate, to fund a specific series of future payments. It is widely used for pension valuations, structured settlements, and comparing lump-sum vs. payment-stream options like lottery payouts.
What is the future value of an annuity?
The future value is the total accumulated value of a series of regular deposits at a future date, including compound interest. It is the core calculation behind 401(k) projections and college savings plans — showing what regular contributions will be worth at a target date.