Retirement calculator

Free growing annuity calculator

See what a stream of growing payments is worth. Enter the first payment, a per-period growth rate, a discount or return rate, and the number of periods. The calculator returns both the present value and the future value of the growing annuity, plus the total paid and the final payment — updated live, as you type.

On this page12 sections

InputsLive

What to compute

First payment (PMT)

Payment growth rate (g)

Discount / return rate (r)

Number of periods (n)

periods

Result

Present value of the growing annuity

$133,316.63

What this growing stream of 20 payments is worth today at a 7% rate.

Present value$133,316.63

Future value$515,893.31

Total nominal paid$268,703.74

Final payment$17,535.06

Estimates only, based on the values you enter. Not financial advice.

Results are estimates. Consult a professional.

Definition

What is a growing annuity?

A growing annuity is a finite series of payments that increase at a constant rate every period. Unlike a level annuity, where every payment is identical, each payment here is a fixed percentage larger than the one before. That growth rate is usually meant to track inflation, a cost-of-living adjustment, an annual raise, or the rising dividend of a maturing company. This growing annuity calculator returns both the present value — what the whole growing stream is worth today — and the future value — what it accumulates to by the end — the moment you enter the first payment, the growth rate, the discount rate, and the number of periods.

It is the natural model for any income stream that does not stay flat. A retiree who wants spending power to keep pace with inflation, a stock priced off a dividend that grows a few percent a year, a lease with an annual escalation clause — all of these are growing annuities. The calculator assumes the first payment lands at the end of period 1 and every later payment is the prior one times (1 + g).

A series of payments over a fixed term that grow at a constant rate g each period.

The amount of the very first payment, made at the end of period 1. Every later payment grows from it.

The constant per-period rate at which each payment exceeds the previous one — often an inflation or raise rate.

The per-period rate used to discount the stream to today (present value) or compound it forward (future value).

The total number of payments in the stream.

Formula

Growing annuity formula

When the rate and the growth rate differ (the usual case), the present and future values of a growing annuity are:

PV = (PMT / (r − g)) × [ 1 − ((1 + g) / (1 + r))^n ]

FV = (PMT / (r − g)) × [ (1 + r)^n − (1 + g)^n ]

FV = PV × (1 + r)^n

The two values are linked: the future value is just the present value compounded forward n periods, FV = PV × (1 + r)^n. So you only ever need one formula plus that bridge. The term (r − g) in the denominator is what makes growing annuities feel unfamiliar — the closer the growth rate gets to the rate, the larger the value becomes, because the payments are nearly keeping pace with discounting.

When r = g exactly, the (r − g) denominator would divide by zero, so the formula takes its limit: PV = n × PMT / (1 + r), and FV = n × PMT × (1 + r)^(n − 1). The calculator handles that edge case automatically, so the result never breaks.

Inputs

The four inputs and how to set them

Every figure the calculator returns comes from four inputs and one toggle. Get these right and the result follows:

First payment (PMT). The size of the first payment only — at the end of period 1. Do not enter an average; the formula grows it from here.
Growth rate (g). The constant rate each payment rises by. For an inflation-protected income, this is your expected inflation rate; for a dividend stream, the expected dividend growth.
Discount / return rate (r). For present value, the rate you discount future money by (often a required return or opportunity cost). For future value, the rate the stream earns.
Number of periods (n). How many payments there are. Keep r and g on the same per-period basis as n — if n counts years, r and g are annual rates.

The Present value / Future value toggle does not change the inputs — it just chooses which result is shown large. Both are always computed, so you can read either at a glance.

Worked example

A worked example using the growing annuity calculator

Example: a $10,000 income that grows 3% a year for 20 years

Priya is modelling an inflation-adjusted retirement income. The first year's withdrawal is $10,000, and she wants it to grow 3% a year to hold its spending power. She discounts at a 7% required return over a 20-year horizon. Here is how the calculator works it through.

Step 1 — Enter the inputs

Priya sets the first payment to $10,000, the growth rate to 3%, the discount rate to 7%, and the number of periods to 20. She leaves the toggle on present value to find today's worth of the stream.

Step 2 — Apply the formula

PV = (10,000 / (0.07 − 0.03)) × [ 1 − (1.03 / 1.07)^20 ]

PV = 250,000 × [ 1 − 0.46673 ]

PV = 133,316.63

Step 3 — Read the result

$133,316.63 present value

That is what Priya's 20-year growing income is worth today at a 7% discount rate. Over the 20 years she actually receives $268,703.74 in nominal payments — the final one reaching $17,535.06 — but discounting brings the today-value down to $133,316.63.

What is this stream worth at the end instead? Switching the toggle to future value compounds the payments forward to year 20, giving $515,893.31 — which is exactly the present value times 1.07^20. All figures here are produced by this calculator using the formula above.

Reference

How a growing annuity's value scales with term

The table follows a $1,000 first payment growing 5% a year, discounted (and compounded) at 8%, as the number of years rises. It shows how the present value, future value, and total nominal payments each pull apart over a longer horizon.

Years (n)	Present value	Future value	Total nominal paid
5	$4,379.47	$6,434.88	$5,525.63
10	$8,183.55	$17,667.68	$12,577.89
15	$11,487.84	$36,441.36	$21,578.56
20	$14,357.99	$66,921.98	$33,065.95
25	$16,851.05	$115,404.01	$47,727.10
30	$19,016.56	$191,357.15	$66,438.85

$1,000 first payment, 5% growth, 8% rate. Figures computed by this calculator.

Notice the present value rises ever more slowly with each added year — distant payments are discounted so hard they barely move the total — while the future value accelerates, because later periods compound on a larger base.

Applications

What a growing annuity is used for

A growing annuity fits any cash-flow stream that rises at a roughly steady rate rather than staying flat. Common uses include:

Inflation-adjusted retirement income — sizing a withdrawal stream that grows with the cost of living, so spending power holds rather than eroding.
Growing dividends — valuing a stock whose dividend is expected to rise a few percent a year over a finite holding period.
Salary and pension streams — present-valuing future earnings or pension payments that include annual raises or cost-of-living adjustments.
Escalating leases and contracts — pricing a lease or service contract with a fixed annual step-up clause.

When the stream never ends, a growing annuity becomes a growing perpetuity (the Gordon-growth model), valued as PMT / (r − g). When payments are level rather than growing, reach for the present value of an annuity or future value of an annuity instead.

Limitations

Gotchas and assumptions

A few assumptions are baked into the growing-annuity formula. Keep them in mind so the result stays meaningful:

Constant growth. Every payment grows at exactly g. Real raises, dividends, and inflation are lumpy — treat the output as a smooth-path estimate.
A constant rate. One discount/return rate applies to every period. Actual market returns and required returns vary over a long horizon.
r and g share a basis. If n counts years, both rates are annual. Mixing a monthly rate with an annual growth rate gives a meaningless answer.
First payment at period end. The formula assumes payment 1 arrives at the end of period 1. A stream that starts immediately is worth (1 + r) times more.
When g exceeds r for a finite annuity the value is still well-defined (the formula simply returns a larger number) — but for a perpetual growing stream, g must be below r or the present value is infinite.

Methodology

Formula source and methodology

The present value of a growing annuity, PV = (PMT / (r − g)) × [1 − ((1 + g)/(1 + r))^n], is a standard time-value-of-money result taught in corporate finance. The calculator evaluates it directly, handles the r = g case with its limit, and derives the future value as PV × (1 + r)^n — so its output matches the standard reference implementations.

Aswath Damodaran, NYU Stern — The Mechanics of Time Value (present value of a growing annuity).Finance Formulas — Present Value and Future Value of a Growing Annuity.

Questions

Frequently asked questions about the free growing annuity calculator

A growing annuity calculator is a free online tool that helps you calculate the present value and future value of a growing annuity — payments that rise at a constant rate g each period. A growing annuity is a finite stream of payments that rise at a constant rate g each period. Its present value discounts that stream to today; its future value compounds it to the end. The first payment lands at the end of period 1. It runs entirely in your browser with instant results and no sign-up.

A growing annuity is a finite series of payments that increase at a constant rate every period, rather than staying level. Each payment is a fixed percentage larger than the one before — typically to track inflation, a cost-of-living adjustment, an annual raise, or a rising dividend. It is the natural model for any income stream that grows steadily over a fixed term.

Use PV = (PMT / (r − g)) × [1 − ((1 + g)/(1 + r))^n], where PMT is the first payment, r is the per-period discount rate, g is the per-period growth rate, and n is the number of periods. For a $10,000 first payment growing 3% a year, discounted at 7% over 20 years, the present value is $133,316.63. When r equals g, the formula takes its limit, PV = n × PMT / (1 + r).

Use FV = (PMT / (r − g)) × [(1 + r)^n − (1 + g)^n], which is the same as the present value compounded forward: FV = PV × (1 + r)^n. The same $10,000 stream growing 3% at a 7% return over 20 years has a future value of $515,893.31. When r equals g, FV = n × PMT × (1 + r)^(n − 1).

A regular (level) annuity pays the same amount every period; a growing annuity's payments rise at a constant rate g. Set g to 0% and a growing annuity collapses to exactly a level ordinary annuity. Growing annuities are used where payments are expected to escalate — inflation-adjusted income, growing dividends, or salaries with annual raises.

For a finite growing annuity, g being greater than r is fine — the formula stays well-defined and simply returns a larger value, because the payments are outpacing the discount. The restriction g < r only applies to a growing perpetuity (an infinite stream), where g must be below r or the present value would be infinite.

About

About this growing annuity calculator

This growing annuity calculator runs entirely in your browser. Every value you enter stays on your device — nothing is sent to a server, logged, or shared. It applies the standard growing-annuity present-value formula, handles the r = g case with its limit, and derives the future value as the present value compounded forward, updating instantly as you type.

Calculators Cloud offers 400+ free tools with no sign-up. The whole Finance calculators shelf includes Present value of an annuity, Future value of an annuity, and Perpetuity tools alongside this one. Or browse the full calculator directory.