How the Growing Annuity Calculator works
A growing annuity is a series of periodic payments that increase by a fixed percentage each period, rather than staying level like an ordinary annuity. It is the standard model behind things like a pension or salary stream that is expected to keep pace with inflation, or a business cash-flow projection where revenue grows at a steady rate. This calculator finds the present value, future value, and total of a growing annuity from the first payment, its growth rate, a discount rate, and the number of payments.
The formula
For a first payment P1, a per-period growth rate g, a per-period discount rate i, and n total payments, the present value of an ordinary growing annuity (payments at the end of each period) is:
PV = P1 × [1 − ((1+g)/(1+i))n] / (i − g)
The future value — what that same stream is worth at the end of the term if reinvested at the discount rate — is:
FV = P1 × [(1+i)n − (1+g)n] / (i − g)
If the discount rate and growth rate are exactly equal, both formulas would divide by zero, so the calculator switches to the limit form instead: PV = P1 × n / (1+i) and FV = P1 × n × (1+i)n−1. Choosing "annuity due" instead of "ordinary annuity" shifts every payment one period earlier, which multiplies both PV and FV by (1+i).
Worked example
Take a first payment of $10,000 growing 3% per period, discounted at 7% per period, over 20 periods. The present value works out to roughly $133,000 and the future value to roughly $516,000. The sum of all 20 payments before discounting — the "total nominal payments" figure — is about $268,700, and the 20th (final) payment alone, after 19 periods of 3% growth, is about $17,500.
Growing annuity versus level annuity
Setting the growth rate to 0% turns the growing-annuity formula into the ordinary level-annuity present value formula, since every payment then equals P1. A growing annuity is always worth more than a level annuity with the same first payment, discount rate, and number of periods, because later payments are larger. It is worth less than a level annuity sized to the growing annuity's final payment, because early payments start out smaller.
What moves the result most
- The gap between growth and discount rate (i − g): a small gap makes the present value large and sensitive to small changes in either rate; a wide gap makes the present value smaller and more stable.
- Number of periods: more periods compound both the growth and the discounting, so present value and future value grow (or shrink) faster than a simple linear scaling as n increases.
- Payment timing: switching from ordinary annuity to annuity due increases present value and future value by a factor of (1+i), reflecting one fewer period of discounting.