Present Value Of Growing Annuity Calculator
What is a stream of payments that grows every period worth today? This calculator values a growing annuity from the first payment, the discount rate, the growth rate, and the number of periods, and it goes further than most: ordinary or annuity-due timing, the future value at the end, an optional growing-perpetuity value, and a period-by-period schedule showing each payment and what it is worth today.
| Period | Payment | Worth today |
|---|
Educational tool, not financial advice. The model assumes a constant growth rate and a constant discount rate for the whole horizon. Real dividends, rents, and salaries rarely grow at a fixed rate, so treat the result as a disciplined estimate, not a prediction.
Quick Answer
A first payment of $5,000 growing 3% a year for 10 years, discounted at 7%, is worth $39,602.63 today as an ordinary annuity. As an annuity due (payments at the start of each year) it is worth $42,374.82. If the payments never stopped and the discount rate beat the growth rate, the stream would be worth $125,000.00. Enter your own numbers above for the full schedule.
Key takeaways
- A growing annuity discounts each payment individually: payment k is P(1+g)k–1, worth P(1+g)k–1/(1+r)k today. The schedule table shows every one.
- When the discount rate equals the growth rate, the standard formula divides by zero but the answer exists: PV = P × n / (1 + r). This tool computes it.
- The growth rate can exceed the discount rate over a finite horizon. Only the never-ending perpetuity needs g below r to stay finite.
- Annuity-due timing is worth exactly (1 + r) more than ordinary timing, because every payment arrives one period earlier.
- Quick Answer
- How to use the growing annuity calculator
- The formula, and the one case that needs a different one
- Worked example: $5,000 growing at 3% for 10 years
- Future value and the growing perpetuity
- Ordinary annuity vs annuity due
- What competing growing-annuity calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the growing annuity calculator
Enter five values and click Calculate. The card is pre-filled with the worked example below, and the results stay hidden until you calculate.
- Enter the first payment, both rates, and the number of periods: the first payment in dollars, the discount rate r and the growth rate g as percents per period, and n as a whole number of periods. All three must use the same period: annual rates mean annual payments and n in years. To use monthly payments with annual rates, divide the annual rates by 12 and express n in months.
- Choose the payment timing: ordinary (end of period) or annuity due (beginning of period). Salary-like streams that pay in arrears are ordinary; rents paid upfront are annuity due.
- Tick the perpetuity box if you want the never-ending value: it shows P/(r – g) when the discount rate exceeds the growth rate, and tells you plainly when no finite value exists.
- Read the results: the present value, a one-line description of the stream, the future value at the final period, the formula the tool used (including the r = g special case), and the period-by-period schedule. Long schedules show the first four periods, an ellipsis, and the last one.
The formula, and the one case that needs a different one
For r ≠ g, the present value is PV = P × [1 – ((1 + g) / (1 + r))n] / (r – g), where P is the first payment, r the discount rate, g the growth rate, and n the number of periods. Each payment is discounted on its own and the geometric series collapses to this closed form, as set out in the annuity chapter of OpenStax Principles of Finance and in Aswath Damodaran's dividend discount models chapter (NYU Stern).
Equal rates (r = g): PV = P × n ÷ (1 + r)
Annuity due: multiply either result by (1 + r)
Growing perpetuity (g < r): PV = P ÷ (r – g)
When r = g, every discounted payment equals P/(1 + r) and there are n of them, so the answer is P × n/(1 + r) with no division by zero. For the perpetuity, the formula only converges when the discount rate beats the growth rate; otherwise the later payments grow faster than discounting can shrink them and the sum has no finite value. The tool states this instead of printing a nonsense number.
Worked example: $5,000 growing at 3% for 10 years
The pre-filled inputs are first payment $5,000, discount rate 7%, growth 3%, 10 periods, ordinary timing. The ratio (1.03/1.07) = 0.962617; raised to the 10th power it is 0.683177; 1 – 0.683177 = 0.316823; divided by (0.07 – 0.03) = 0.04 gives 7.92058; times $5,000 gives $39,602.63. Type these numbers into the card and you get the same figure, plus the schedule below it.
Growth compounds the payments while discounting shrinks their present worth. The first five payments of the example, and what each is worth today:
Bar length shows each payment's worth today relative to the $4,672.90 first payment. Payments keep growing, but discounting wins the race when r beats g.
Future value and the growing perpetuity
Present value answers "what is it worth today?" Two related questions come free with the same inputs. The future value compounds the present value forward: FV = PV × (1 + r)n. In the worked example that is $39,602.63 × 1.0710 = $77,904.37 at the end of year 10. The growing perpetuity asks what the stream would be worth if the payments never stopped:
Growing annuity, 10 payments
$39,602.63
Finite horizon. Works for any growth rate, even above the discount rate, because the sum stops.
Growing perpetuity, forever
$125,000.00
P / (r – g) = $5,000 / 0.04. Only finite when the discount rate exceeds the growth rate.
The perpetuity is the limit of the annuity as n grows: set n very large in the tool and the ordinary result converges toward $125,000. This is also the Gordon growth model from stock valuation, which prices a share as next year's dividend divided by (r – g); Myron Gordon's original 1959 paper "Dividends, Earnings, and Stock Prices" is the primary source, and the dividends calculator covers the dividend side of that analysis.
Ordinary annuity vs annuity due
An ordinary growing annuity pays at the end of each period: the first $5,000 arrives one full period from now and is discounted once. An annuity due pays at the beginning: the first payment arrives immediately, is never discounted, and every later payment is discounted one period less. The due value is therefore the ordinary value times (1 + r): $39,602.63 × 1.07 = $42,374.82. Switch the timing selector in the card to see both. If you are valuing a stream with no growth at all, the present day value calculator handles the plain annuity case, and premium payouts covers annuity-style income streams.
What competing growing-annuity calculators miss
Most growing-annuity tools compute the present value and stop. The gaps, checked against the top-ranking pages:
- Formula references without a real tool (CalculatorSoup's annuity page): superb derivations, including the r = g and perpetuity cases, but you do the arithmetic yourself. Ours runs all of it, including the edge case, from one set of inputs.
- Worked tables without interactivity (Annuity Expert Advice): correct sample numbers but fixed scenarios. Ours lets you change every input and shows the full payment schedule, not just the headline.
- Thin formula pages (Calculator Hive and similar): the closed form and nothing else: no timing choice, no future value, no perpetuity, no schedule, no handling of r = g.
- Spreadsheet tutorials (Spreadsheet Planet): useful if you live in Excel, but a five-step manual process for one answer. Nothing you can open on a phone.
- The gap this page fills: present value, future value, and perpetuity from one set of inputs, ordinary and annuity-due timing, an explicit r = g formula, honest handling of g above r, and a period-by-period schedule that shows its working.
Frequently asked questions
How much a stream of payments that grows at a fixed rate is worth today, after discounting each payment at your required rate of return. It is the lump sum you could accept now in exchange for the whole stream.
The standard formula divides by zero, but the answer exists: PV = P x n / (1 + r). Every discounted payment equals P / (1 + r), and there are n of them. Example: $1,000 first payment, 5% growth and 5% discount, 10 periods gives $9,523.81. This tool computes it automatically.
A growing annuity has a fixed number of payments n. A growing perpetuity never ends, and its value is P / (r - g), which requires the growth rate to stay below the discount rate to remain finite. Set n very large in this tool and the ordinary result converges toward the perpetuity value.
Yes, over a finite horizon. The closed form is valid for any r other than g; when g exceeds r the present value is simply larger, because the payments outgrow the discounting. For example, $1,000 growing at 5% for 10 years discounted at 2% is worth $11,208.70. Only the never-ending perpetuity needs g below r.
Yes. Every payment arrives one period earlier and is therefore discounted less. The difference is exactly one period of discounting: multiply the ordinary value by (1 + r). In the worked example, the ordinary value of $39,602.63 becomes $42,374.82 as an annuity due at 7%.
Closely related. The Gordon model values a stock as D / (r - g), which is exactly the growing-perpetuity limit of this formula with the first dividend as P. It suits mature companies with steady dividend growth; faster-growing companies need a multistage model instead.
Only after converting: divide the annual rates by 12 and express n in months. The tool needs r, g, and n in consistent per-period units, so mixing annual rates with a monthly period count gives a wrong answer.
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References
- OpenStax, Rice University. Principles of Finance. Accessed October 23, 2026.
- Damodaran, Aswath (NYU Stern School of Business). Dividend Discount Models (PDF). Accessed October 23, 2026.
- Damodaran, Aswath (NYU Stern School of Business). Investment Valuation, Chapter 13: Dividend Discount Models (PDF). Accessed October 23, 2026.
- Gordon, M. J. "Dividends, Earnings, and Stock Prices", The Review of Economics and Statistics, Vol. 41, No. 2 (1959), pp. 99-105. Accessed October 23, 2026.
- Khan Academy. Present value. Accessed October 23, 2026.
- Maths is Fun. Present Value. Accessed October 23, 2026.
- U.S. Department of the Treasury. Interest Rate Statistics: Daily Treasury Par Yield Curve Rates. Accessed October 23, 2026.
- Board of Governors of the Federal Reserve System. H.15: Selected Interest Rates. Accessed October 23, 2026.
- U.S. Department of the Treasury. Daily Treasury Rate Archives. Accessed October 23, 2026.
- University of Pittsburgh, Katz Graduate School of Business. Growing Annuity (present value of a growing annuity: formula and worked example). Accessed October 23, 2026.