Annuity math, in short
In finance, an "annuity" simply means a series of equal payments made at regular intervals — a loan payment, a lease payment, a savings deposit. This calculator finds one of three things about that series: what it's worth today (present value), what it grows to by the end (future value), or how big each payment needs to be. Whether payments land at the end of each period (ordinary annuity) or the start (annuity due) changes the answer, since each due payment sits in the account one period longer.
Key takeaways
- $1,000 paid every period for 20 periods at 5% has a present value of about $12,462 and a future value of about $33,066.
- Switching that same stream from ordinary to due — payments at the start instead of the end of each period — raises the present value by about $623 and the future value by about $1,653.
- Moving the rate from 5% to 6% on that 20-period, $1,000 stream raises the future value from about $33,066 to about $36,786 — proof that rate assumptions matter more the longer the timeline runs.
- This is the same math used to price loan payments, lease payments, and the accumulation phase of an insurance annuity — but this tool doesn't model insurance-specific fees, surrender charges, or riders.
What present value and future value mean here
Present value asks: what is this whole series of future payments worth if I had it as one lump sum today? Future value asks the opposite: if I keep making these payments and let them earn interest, what do they add up to by the end? Both answers depend on the same three inputs — the payment amount, the rate per period, and the number of periods — just solved in opposite directions.
The four things this calculator can solve for
Using the calculator's defaults — $1,000 per period, 5% per period, 20 periods, ordinary annuity — the two core formulas work out to:
PV = PMT × [(1 − (1+r)^-n) / r] = $1,000 × 12.462 ≈ $12,462.21
FV = PMT × [((1+r)^n − 1) / r] = $1,000 × 33.066 ≈ $33,065.95
The calculator can also flip either formula around to solve for the payment — useful when you know how much you need to end up with (or start with) and want to work out what each period's payment has to be to get there.
Ordinary annuity vs. annuity due
An ordinary annuity pays at the end of each period — this is how most loans, bonds, and mortgages work. An annuity due pays at the start of each period — rent and insurance premiums are usually structured this way. Because a due payment sits earning interest for one extra period compared to the ordinary version, both its present and future value are simply the ordinary result multiplied by (1 + rate):
PV (ordinary): $12,462.21 → PV (due): $13,085.32 — about $623 more
FV (ordinary): $33,065.95 → FV (due): $34,719.25 — about $1,653 more
Getting the timing setting right matters — mixing them up on a real calculation, like comparing lease quotes, will make one option look better than it actually is.
Why the rate matters more over long timelines
A one-point rate change looks small until it's compounding across many periods. Take that same $1,000-per-period, 20-period stream and raise the rate from 5% to 6%: future value climbs from about $33,066 to about $36,786 — a difference of roughly $3,720 from one percentage point. Extend the number of periods further and that gap widens even faster, which is why the rate assumption deserves as much scrutiny as the payment amount when you're planning years or decades out.
This calculator vs. an insurance annuity
"Annuity" has two common meanings, and it's easy to mix them up. In finance and accounting, it just means a series of equal payments — the sense this calculator uses. Insurance companies also sell products they call annuities: contracts where you pay in (often as a lump sum) and receive income later, typically in retirement. Those contracts run on the same present-value and future-value math underneath, but they add fees, surrender charges, riders, and tax rules this tool doesn't model. If you're sizing up a payout from savings you already have, the annuity payout calculator is the closer fit; if you're shopping an actual insurance annuity contract, treat this as a starting point for the math, not a substitute for the contract's disclosures.
Related calculators
For a single lump sum instead of a payment stream, the present value calculator and future value calculator handle the simpler one-time-amount version of this math. The compound interest calculator is useful for irregular contribution schedules, and the retirement calculator puts this kind of projection into a full retirement-income context.