Distinct from a level annuity — a growing annuity’s payment increases by a fixed growth rate each period, common in pensions with cost-of-living adjustments or leases with scheduled rent increases.
How it works
Each future payment is discounted back to today at the discount rate, after growing from the first payment at the growth rate — summed algebraically into a single present value formula, using a special case when the growth and discount rates are equal.
What this does not include
This models a *finite* number of periods — this site’s separate terminal-value and perpetuity calculators handle the growing payment stream that continues forever instead.
How to use this calculator
- Enter the first payment, growth rate, discount rate, and number of periods.
A worked example
A first payment of $10,000, growing 3% annually, discounted at 8%, over 10 periods: present value = $75,501.34.
What the variables mean
| Variable | Meaning |
|---|---|
| First payment | The initial cash flow, one period from now |
| Growth rate | Annual percentage growth in each subsequent payment |
| Discount rate | Rate used to discount future payments to present value |
| Periods | Number of payments |
Edge cases worth knowing
A growth rate that exceeds the discount rate makes standard growing annuity math break down — the growing perpetuity version of this formula requires growth strictly below the discount rate to converge, though this fixed-period version still returns a result as long as periods are finite.
Zero periods makes the calculation meaningless — there are no payments to value, so the calculator declines to show a result for that input.
Frequently asked questions
What’s a real-world example of a growing annuity?
A pension with an annual cost-of-living adjustment, or a multi-year lease with scheduled annual rent increases, both pay a growing stream of payments over a fixed term.
What happens when the growth rate equals the discount rate?
The standard formula divides by zero in that case — a special-case formula (payment times periods, discounted one year) is used instead.
How is this different from the growing perpetuity used in terminal value?
A growing annuity has a defined end date; a growing perpetuity (used in this site’s terminal-value calculator) continues the growing payments forever.
