The Concept
What is a growing annuity?
A growing annuity is a series of payments that increases by a fixed percentage every period, instead of staying flat. Ordinary annuities pay the same amount each time; a growing annuity starts at a first payment and steps it up year after year. It is the natural model for money that rises over time — retirement contributions that grow with a salary, income indexed to inflation, or a dividend stream that increases each year.
The future value is what that rising stream of payments accumulates to once every payment has earned compound interest to the end of the term. Because later payments are larger, a growing annuity finishes well ahead of a level one at the same starting amount. For level payments instead, this calculator's parent-tier sibling is the future value of annuity calculator.
The Timing
Ordinary vs annuity due
As with any annuity, timing shifts the result, and the toggle at the top handles both:
- Ordinary annuity — each growing payment lands at the end of the year. This is the default.
- Annuity due — each payment lands at the beginning of the year, so every payment earns one extra year of interest and the total is higher.
With a $10,000 first payment growing 3 percent a year at 7 percent interest over 20 years, ordinary timing reaches about $515,893, while annuity-due timing lifts it to about $552,006. The difference is the extra year of compounding every payment receives.
How To
How to use this calculator
Set the timing, then fill in four inputs:
- First payment — the amount of the very first payment, before any growth is applied.
- Annual interest rate — the yearly rate of return the balance earns.
- Annual payment growth — how much each payment rises versus the year before.
- Number of years — how long the growing payments continue.
The result splits the future value into what you paid in and the interest earned on top. The year-by-year breakdown shows both the rising payment and the accumulating balance, so you can watch the growth compound on two fronts at once.
The Formula
The growing annuity formula
The future value of a growing ordinary annuity is:
FV = C × [ ((1 + r)n − (1 + g)n) ÷ (r − g) ]
where C is the first payment, r is the interest rate per period, g is the payment growth rate per period, and n is the number of periods. An annuity due multiplies the whole result by an extra (1 + r). There is one special case: when the interest rate exactly equals the growth rate, the denominator (r − g) becomes zero and the formula breaks down. The calculator detects that and switches to the limit form:
FV(r = g) = C × n × (1 + r)n − 1
which gives the correct answer when the two rates match. The single-sum math underneath is the same growth captured in the future value formula guide.
Example
Example: payments that grow 3% a year
Here is a $10,000 first payment growing 3 percent a year, earning 7 percent, as an ordinary annuity. Watch both columns climb — the payment rises each year, and the balance compounds on top of it.
| Year | Payment that year | Balance |
|---|
| 5 years | $11,255 | $60,819 |
| 10 years | $13,048 | $155,809 |
| 15 years | $15,126 | $300,266 |
| 20 years | $17,535 | $515,893 |
By year 20 the payment has grown from $10,000 to about $17,535, and the balance reaches roughly $515,893 — of which about $268,704 is payments and the rest is interest.
Real World
Where growing annuities show up
Rising payment streams are common, which is what makes the growing annuity a useful model:
- Salary-linked saving. If you save a fixed percentage of pay and your pay rises each year, your contributions form a growing annuity.
- Inflation-indexed income. Pensions or payouts that step up with inflation grow at a set rate each year.
- Escalating investment plans. Some investors deliberately raise their annual contribution to keep pace with income or cost of living.
In each case the growth rate is the yearly step-up, and the interest rate is the return the accumulated balance earns.