Growing Annuity Calculator
A growing annuity is a run of payments made for a fixed number of periods, where each payment is bigger than the one before by a constant growth rate. This calculator finds its present value: what that stream of rising payments is worth in today's money. Many real cash flows behave this way, including a salary that climbs with inflation, a commercial lease with annual escalations, or dividends expected to grow at a set pace for a known window. The value is finite because the stream ends after a fixed number of years, and because each future payment is discounted more heavily than the last. When the discount rate differs from the growth rate, the present value uses the standard growing annuity formula; when the two rates happen to be equal, a special-case version takes over to avoid dividing by zero. Enter your first payment, the discount rate, the growth rate and the number of years to value retirement income, escalating leases, or the explicit forecast period of a discounted cash flow analysis. Every figure here is computed deterministically from the formula shown below, never estimated, and the worked example reconciles exactly to the calculator's default inputs so you can follow each step yourself with confidence.
A growing annuity pays a rising amount for a set number of years. A first payment of $1,000 growing 3% a year for 10 years, discounted at 8%, has a present value of $7,550.13.
Growing annuity formula
When r is not equal to g:
PV = ( PMT / (r - g) ) x ( 1 - ((1 + g) / (1 + r))^n )
When r equals g:
PV = PMT x n / (1 + r)
PMT = first payment, r = discount rate, g = growth rate, n = number of years
The ratio (1 + g) / (1 + r) raised to the power n captures how much value sits in payments beyond the final year. Subtracting it from one and scaling by PMT / (r - g) trims the growing perpetuity down to a stream that stops after n years. When the two rates match, the ratio equals one and the main formula would divide by zero, so the equal-rate version is used.
Worked example
A payment stream starts at 1,000 at the end of year 1, grows 3% a year, runs for 10 years, and is discounted at 8% a year. Because the discount rate and growth rate differ, use the main formula.
- PMT / (r - g) = 1,000 / (0.08 - 0.03) = 1,000 / 0.05 = 20,000
- (1 + g) / (1 + r) = 1.03 / 1.08 = 0.953704
- 0.953704^10 = 0.622493
- 1 - 0.622493 = 0.377507
- PV = 20,000 x 0.377507 = 7,550.13
The present value is 7,550.13. These are the calculator's default inputs, so the result above matches the widget exactly.
How term and growth change the present value
Present value of a stream that starts at 1,000, discounted at 8% per year, for the rows below.
| Years | Growth 0% | Growth 3% | Growth 5% |
|---|---|---|---|
| 5 | 3,992.71 | 4,220.35 | 4,379.47 |
| 10 | 6,710.08 | 7,550.13 | 8,183.55 |
| 20 | 9,818.15 | 12,250.04 | 14,357.99 |
Time value of money concepts: US Securities and Exchange Commission, Investor.gov.
Growing annuity calculator: frequently asked questions
What is a growing annuity?
A growing annuity is a series of payments made for a fixed number of periods where each payment is larger than the last by a constant growth rate. It models cash flows that climb steadily, such as a salary that rises with inflation, a lease with built-in escalations, or dividends expected to grow at a fixed pace for a set window before levelling off.
How is the present value of a growing annuity calculated?
When the discount rate r differs from the growth rate g, present value equals the first payment divided by (r - g), multiplied by one minus the ratio (1 + g) over (1 + r) raised to the number of periods. When r and g are equal, that formula breaks down, so the special case present value is the payment times the number of periods, divided by (1 + r).
How is a growing annuity different from a growing perpetuity?
Both have payments that grow at a fixed rate, but a growing annuity stops after a set number of periods while a growing perpetuity continues forever. A growing perpetuity's present value is simply the payment divided by (r - g). A growing annuity is worth less because it ends, so its formula multiplies that base by a factor that trims off the value of all payments beyond the final period.
Does the growth rate have to be smaller than the discount rate?
Unlike a growing perpetuity, a growing annuity gives a finite present value even when the growth rate exceeds the discount rate, because the payment stream is limited to a fixed number of periods. The calculator handles all three cases: growth below the discount rate, growth above it, and the special case where the two rates are equal.
Where is the growing annuity formula used?
It values retirement income that rises with inflation, escalating commercial leases, structured settlement payments, and the explicit forecast period of a discounted cash flow valuation where cash flows grow before a terminal value is applied. Any time payments rise at a steady rate for a known length of time, the growing annuity present value gives their worth in today's money.
Official sources
- Time value of money, present value and investing basics: US Securities and Exchange Commission, Investor.gov. As at 24 June 2026.
Reviewed by the CalculatorHub team, edited by James Graham, 24 June 2026. See our methodology. This is general information, not financial, tax, legal or investment advice.