How this instrument works
A growing annuity is a series of payments made at equal intervals where the payment itself gets bigger by a fixed percentage every time, rather than staying flat the way a level annuity does. First payment, $ sets what lands at the end of period one; Payment growth rate, % is the fixed step every later payment takes over the one before it; Discount/return rate, % is what the money earns once it is paid in; Number of periods is how many payments run in total. A pension actuary pricing a cost-of-living-adjusted benefit, an HR analyst modeling a salary that gets a scheduled annual raise, and a landlord valuing a lease with a written rent-escalation clause all size a stream this same way — payments that step up on a known schedule rather than repeat unchanged.
The formula splits into two separate compounding paths and takes their difference. (1 + r) raised to the number of periods is how a flat, non-growing $1 would compound if invested for the whole term; (1 + g) raised to the same power is how big the payment schedule itself would be after that many growth steps, with no interest involved at all. Subtracting the second from the first and dividing by the gap between the two rates, r − g, collapses what would otherwise be a period-by-period sum of every payment's own separate compounding into one closed-form line. That subtraction only works because the rate and the growth rate stay constant and distinct for the entire term — set them equal and the denominator hits zero, which is why the sheet blocks that input rather than returning a number.
This is a future-value, finite-horizon question, not the present-value, infinite-horizon one a dividend discount model asks. The Gordon Growth calculation elsewhere on this site prices a share by discounting a dividend stream assumed to grow forever, back to a single value today; this instrument instead compounds a payment stream that grows for a fixed, countable Number of periods forward to a single value at the end. Nothing here forecasts whether the growth rate is realistic — a salary raise, a rent escalator, or a COLA that has run at 3% for a decade can slow, stop, or reverse, and the formula has no opinion on which.
- Enter the amount paid at the end of period one into First payment, $.
- Set Payment growth rate, % to the fixed percentage each later payment grows over the one before it.
- Set Discount/return rate, % to what the money earns once it is paid in — this must differ from the growth rate.
- Type the total number of payments the schedule runs for into Number of periods.
- Check Future value of the growing annuity to see the compounded total once the final, largest payment has landed.
Worked example — a $1,000 payment growing 3% a year
Set First payment, $ to 1000, Payment growth rate, % to 3, Discount/return rate, % to 8, and Number of periods to 10 — a $1,000 payment at the end of period one, each later payment 3% bigger than the one before it, the whole stream earning an 8% return along the way. Future value of the growing annuity reads $16,300.17.
Run the identical $1,000, 8%, and 10 periods through a level-payment annuity instead, with Payment growth rate, % held at zero, and the total lands at $14,486.56 — over $1,800 lower, purely because none of those ten payments ever step up. A raise that only keeps pace with a mild 3% drift, applied consistently across a ten-period stream, is worth more than eighteen hundred dollars against a flat schedule earning the identical 8% return.
Questions
How is a growing annuity different from a regular annuity?
A regular annuity pays the same fixed amount every period; a growing annuity's payment gets bigger by Payment growth rate, % each time. On the worked example, a flat $1,000 stream at 8% over 10 periods reaches $14,486.56, while the same stream growing 3% a period reaches $16,300.17 — the extra value comes entirely from later payments outgrowing the first.
Who actually uses this calculation?
A pension actuary pricing a benefit with a built-in cost-of-living adjustment, an HR team modeling what a salary track worth a scheduled annual raise compounds to, and a commercial landlord or tenant valuing a multi-year lease with a written rent-escalation clause all size a rising payment stream this same way, rather than treating it as level.
Why must Discount/return rate, % and Payment growth rate, % be different numbers?
The formula divides by the gap between the two rates, r minus g. Set them equal and that gap is zero, which makes the division undefined rather than producing a real future value — the sheet blocks the equal case for that reason. A real schedule where growth caught up exactly to the return needs a different formula entirely, not this one with a zero denominator.
How is this different from a growing perpetuity or a dividend discount model?
This instrument compounds a payment stream forward to a future value over a fixed, countable Number of periods. A growing perpetuity, the shape behind a dividend discount model, instead discounts a payment stream assumed to grow forever back to a present value today. Set Number of periods high enough here and the two ideas converge, but the dividend discount model never asks for a period count at all.
Can Payment growth rate, % be negative?
Yes — a negative value means each payment shrinks instead of grows, useful for a royalty or a declining benefit expected to fall by a fixed percentage every period. The formula runs exactly the same arithmetic either way; only the sign of g changes, and the result must still satisfy r not equal to g.
What does this arithmetic leave out?
It assumes Discount/return rate, % and Payment growth rate, % both hold perfectly constant for every one of the Number of periods, with no missed or delayed payment and no fees or taxes taken out along the way. A real raise, escalator, or COLA can run faster or slower than assumed, or stop outright — treat the output as a clean benchmark for a perfectly steady schedule, not a claim about how any single raise or lease will actually unfold.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.