Annuity Calculator
Calculate present and future value of equal periodic payments.
Formula
PV = PMT×[(1-(1+r)^-n)/r]
Example
$1,000/month at 0.5% for 120 periods → PV ≈ $90,073.
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Understanding the Annuity
An annuity is just a stream of equal payments, and its whole logic rests on one uncomfortable truth: a dollar you'll receive in ten years is worth less than a dollar today. This calculator shows both what a payment stream is worth now (present value) and what it grows into later (future value).
How it actually works
Enter the payment per period, the rate per period, and how many periods run. Present value discounts every future payment back to today; future value compounds them forward. A $1,000 monthly payment for 20 years at 0.5%/month has a present value near $139,600 — that's what the whole stream is worth today — but a future value over $462,000 once compounding does its work.
| Rate per period | Present value | Future value |
|---|---|---|
| 0.25%/mo | $188,000 | $332,000 |
| 0.50%/mo | $139,600 | $462,000 |
| 0.75%/mo | $105,700 | $652,000 |
The deeper context most people miss
The gap between present and future value is the entire point of the time value of money. Insurers selling you an annuity quote the monthly payout; what they don't advertise is the discount rate baked into the price. A higher assumed rate means they can offer a bigger payment for the same premium — which is why annuity quotes swing so much with interest rates. When rates are high, fixed annuities suddenly look generous.
The centuries-old math behind annuities
Annuities are among the oldest financial instruments — Roman soldiers received annua, annual stipends, and 17th-century governments sold life annuities to fund wars. The pricing problem they created drove the birth of actuarial science: Edmond Halley (of comet fame) built one of the first mortality tables in 1693 specifically to value annuities fairly. The present-value math this calculator uses is the direct heir of that work. Every time you discount a future payment stream to today's value, you're applying a technique refined over three centuries to answer one question insurers and pension funds still wrestle with: what is a promise of future money worth right now?
A third example: comparing two retirement offers
Suppose at 65 you're offered two ways to take a pension: a lump sum of $400,000, or $2,400 a month for life. Translate the monthly payments into a stream and value them. At a 4% annual discount rate over a 25-year life expectancy, the present value of $2,400/month is roughly $455,000 — higher than the $400,000 lump sum, suggesting the payments are the better deal if you live to about 90. But shift the assumptions: if you expect a shorter life or can invest the lump sum at more than 4%, the lump sum can win. This is exactly the calculation pension holders face and frequently get wrong by comparing the monthly payment to nothing, or the lump sum to nothing, instead of valuing them against each other. The annuity's hidden advantage is that it doesn't stop at 25 years — it pays as long as you live, which is insurance against the real risk of outliving your money that a lump sum, however well invested, can't fully replicate.
Reading an annuity quote critically
When an insurer offers you $1,500/month for life in exchange for a $250,000 premium, run the numbers backward. That's $18,000 a year, an implied simple yield of 7.2% — but that figure includes return of your own principal, not just growth. The real question is how long you'll live to collect. Break-even is roughly 14 years; live to 90 and it's a strong deal, pass earlier and the insurer wins. Compare the guaranteed payment against what a conservative withdrawal from the same $250,000 invested yourself would produce, and weigh the annuity's insurance against longevity risk. Annuities aren't investments so much as insurance against outliving your money — priced accordingly.
Present value versus future value in a real decision
Suppose you're offered $2,000 a month for 15 years at an assumed 0.4% monthly rate. The future value — what it compounds to if you invested each payment — is about $530,000. But the present value, what that whole stream is worth today, is only about $271,000. Which number matters depends on your question. If you're deciding whether to accept the annuity or a lump sum, compare the lump sum to the present value: a $250,000 lump sum is worse than this annuity's $271,000 present value, so the payments win. If you're planning what you'll have accumulated for a future goal, the future value is your figure. Confusing the two is how people misjudge annuity offers — the insurer quotes whichever framing sells best.
Variations: fixed, variable, immediate, and deferred
The word 'annuity' covers several very different products, and the math shifts with each. A fixed annuity pays a guaranteed amount, which is what this calculator models. A variable annuity ties payments to the performance of underlying investments, so the future value swings with markets and the guarantees come with fees. An immediate annuity begins paying right after you hand over the premium — useful at retirement — while a deferred annuity accumulates for years before payments start, adding a growth phase before the payout phase. Ordinary annuities pay at the end of each period; annuities due pay at the start, making each payment worth slightly more. Insurers layer riders, surrender charges, and mortality assumptions on top, which is why two annuities quoting the same monthly figure can represent wildly different value. The present-value math here is the neutral yardstick: whatever the product's bells and whistles, discounting the actual promised cash flows to today reveals what you're really being sold.
Using the two values to make the call
The practical skill is knowing which value answers your actual question. If someone is selling you an annuity, compute the present value of the payment stream at a realistic discount rate and compare it to the premium they're charging — if the premium exceeds the present value, you're overpaying for the guarantee. If you're building toward a goal, the future value tells you what a stream of contributions will accumulate to. And if you're comparing an annuity offer to managing the money yourself, translate the monthly payment into an implied yield and stack it against what a conservative withdrawal from the same principal would produce. The one factor the math can't capture is longevity: an annuity is insurance against outliving your savings, and that protection has real value even when the raw numbers look unexciting. Run the present value first to check you're not overpaying, then decide whether the longevity insurance is worth the premium over simply investing the lump sum yourself. That two-step keeps you from being dazzled by a large monthly figure that's mostly a return of your own capital.
What people get wrong
- Confusing an ordinary annuity (payments at period end) with an annuity due (payments at the start) — the timing difference compounds into real money.
- Treating the advertised payout as 'return' without accounting for the principal you handed over.
- Ignoring inflation — a fixed $1,000/month feels very different 20 years in.
Where the math comes from
Present value = P·[1 − (1+r)^−n] / r and future value = P·[(1+r)^n − 1] / r, where P is the payment, r the rate per period, and n the number of periods. These are the closed-form sums of a geometric series of discounted (or compounded) payments — the foundation of every pension and bond valuation.
Questions and answers
What is a realistic long-term return rate?
US large-cap equities have returned ~10% nominal and ~7% real since 1928. For projections, 6-7% nominal is conservative; 8-9% is the historical average for US-tilted portfolios.
How does inflation affect long-term projections?
Use real returns (return minus inflation) for inflation-adjusted projections. A nominal $1M in 30 years has the purchasing power of about $412K today at 3% inflation.
Should I include dividends?
Yes - total return (price appreciation + dividends reinvested) is the right number. Using only price appreciation undercounts equity returns by ~1.5-2 percentage points annually.
How do fees affect the projection?
A 1% expense ratio compounds to roughly 25% less ending balance over 40 years. Low-cost index funds typically charge 0.03-0.20%; actively managed funds 0.5-1.5%.
What happens during bear markets?
Markets recover - historically every drawdown has eventually been followed by a higher peak. The math of compounding actually rewards consistent buying through downturns.
Should I take a lump sum or the annuity payments?
It hinges on the implied return and your longevity. Divide the annual payments by the lump sum offered — if that yield beats what you could safely and reliably earn elsewhere, the annuity may be the stronger choice, especially because it removes the risk of outliving your savings. But a lump sum you control can be invested for potentially higher returns, left to heirs, or spent flexibly in an emergency, none of which a fixed annuity allows. Compute the present value of the payment stream at a realistic discount rate and compare it directly to the lump sum; if the present value is higher, the payments are mathematically worth more. Then weigh the intangibles: your health and family longevity, your comfort managing money, and how much you value a guaranteed income you can't outlive. There's no universal answer, only the one that fits your situation.
What's the difference between an annuity due and an ordinary annuity?
An ordinary annuity pays at the end of each period, while an annuity due pays at the beginning. That timing difference matters because money received earlier can be invested or spent sooner, so each annuity-due payment is worth exactly one period's interest more than the equivalent ordinary-annuity payment. Over many periods that compounds into a meaningful gap in both present and future value. Rent is the classic annuity due — you pay for the month at its start — while a bond's coupon is an ordinary annuity, paid at period end. When comparing annuity products or valuing a payment stream, always check which type you're dealing with, because assuming the wrong one throws off the valuation by a full period's worth of interest, which on a long stream is real money.
Sources & References
Authoritative references consulted in building this calculator and educational content. These are primary sources — check directly for the most current figures.
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