Growing annuities model anything that increases steadily. If the growth rate exceeds the discount rate, the present value grows without limit as payments are added, which is why a perpetuity needs r > g.
How to use the Growing Annuity Calculator
- First payment
- Growth rate per period
- Interest rate per period
- Number of periods
- Payments made at
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the first payment, the growth rate per period, the interest (discount) rate per period, the number of periods and the timing.
Inputs explained
| Field | What to enter |
|---|---|
| First payment | Amount in your currency |
| Growth rate per period | In % |
| Interest rate per period | In % |
| Number of periods | A number |
| Payments made at | Choose one: End of each period, Beginning of each period |
What each result means
- Present value = gpv([Interest rate per period]÷100, [Number of periods], [First payment], [Growth rate per period]÷100, [Payments made at])
- Future value = gfv([Interest rate per period]÷100, [Number of periods], [First payment], [Growth rate per period]÷100, [Payments made at])
- Last payment = [First payment]×(1 + [Growth rate per period]÷100)^([Number of periods] – 1)
Example values
How the main result changes when First payment changes and everything else stays at the example values above:
| First payment | Present value |
|---|---|
| 500 | 8,535.88 |
| 750 | 12,803.82 |
| 1,000 | 17,071.75 |
| 1,250 | 21,339.69 |
| 1,500 | 25,607.63 |
| 2,000 | 34,143.51 |
Formula
PV = P₁ × (1 − ((1 + g) ÷ (1 + r))^n) ÷ (r − g)
FV = P₁ × ((1 + r)^n − (1 + g)^n) ÷ (r − g)
If r = g: PV = n × P₁ ÷ (1 + r)
Worked example
Inputs: First payment: $1,000; Growth rate per period: 3 %; Interest rate per period: 6 %; Number of periods: 25; Payments made at: End of each period.
Results: Present value = $17,071.75; Future value = $73,269.76; Last payment = $2,032.79; Total payments = $36,459.26.
Frequently asked questions
What is a growing annuity?
Payments that increase at a constant rate each period.
What if growth equals the interest rate?
PV = n × P₁ ÷ (1 + r).
Where are growing annuities used?
Pensions with COLAs, rising savings plans and valuing growing cash flows.