What this calculator does
A growing annuity is a fixed number of payments that increase at a constant rate, which describes a great many real situations: a salary with annual rises, a lease with indexed rent, or a pension with cost-of-living adjustments.
The growth matters more than it first appears. A $10,000 payment growing at 3 per cent reaches $17,535.06 by period 20, and the twenty payments total $268,703.74 undiscounted, though they are worth $122,500.41 today at an 8 per cent discount rate.
The formula
The formula divides the first payment by the difference between the discount and growth rates, then multiplies by a term that truncates the stream at the chosen number of periods rather than letting it run forever.
| Term | Meaning |
|---|---|
| Growing annuity | A finite series of payments increasing at a constant rate. |
| First payment | The payment at the end of the first period, which the growth builds from. |
| Discount rate | The rate used to bring future payments back to present value. |
The inputs explained
| Field | What to enter |
|---|---|
| First payment (next period) ($) | The first payment, received at the end of the next period. |
| Discount rate (%) | The discount rate per period. |
| Growth rate per period (%) | The growth rate per period. It may exceed the discount rate here, unlike a perpetuity. |
| Number of periods | The number of payments. |
When to use it
Valuing a salary stream
Employment income with regular rises is a growing annuity, which makes it valuable for comparing offers.
Pricing an indexed lease
Commercial leases with annual CPI increases fit this pattern exactly.
Planning a rising withdrawal
Retirement drawdowns often need to increase with inflation to hold purchasing power.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the number of payments change the value?
The same payment stream over three durations.
| Number of periods | Present value | Total of all payments, undiscounted |
|---|---|---|
| 10 periods | $75,501.34 | $114,638.79 |
| 20 periods | $122,500.41 | $268,703.74 |
| 30 periods | $151,757.03 | $475,754.16 |
Questions
How is this different from a growing perpetuity?
A perpetuity runs forever and requires the discount rate to exceed the growth rate. A growing annuity stops after a set number of payments, so growth may exceed the discount rate without the value running away.
What happens if growth equals the discount rate?
The standard formula divides by zero, so the calculator reports it as undefined. Mathematically the answer in that case is simply the first payment multiplied by the number of periods, discounted once.
Why is the present value so much less than the total paid?
Because payments in later periods are discounted by a compounding factor. At 8 per cent, a payment thirty periods out is worth about a tenth of its face amount today, which is why extending the term adds so little value.
Does the first payment occur now or next period?
Next period. This is an ordinary annuity convention. If payments start immediately, the whole value is one period less discounted, which makes it larger.
For a stream with no end date, see the perpetuity calculator. For discounting a single sum, see the present value calculator.