Growing Annuity Calculator (present & future value of payments that rise each period)

Understanding the growing annuity calculator — concept and principle

This calculator values a series of payments that grow by a fixed percentage each period. It gives the present value, the future value at the end, the sum of all payments, the last payment, the difference between total payments and present value, and the value of a growing perpetuity if the payments never stopped. Use it for pensions with indexation, rising rents or salaries, retirement income planning and finance courses.

Later payments are bigger but discounted more, so their present values shrink.

How it is calculated

With first payment P, growth g, rate r and N payments at the end of each period:

PV = P ÷ (r − g) × [1 − ((1 + g) ÷ (1 + r))^N]; if r = g, PV = N × P ÷ (1 + r).
Annuity due (payments at the start): PV × (1 + r).
Future value at the end = PV × (1 + r)^N.
Sum of payments = P × ((1 + g)^N − 1) ÷ g.
Last payment = P × (1 + g)^(N − 1).
Growing perpetuity (r > g) = P ÷ (r − g).

The principle

Each payment is discounted back to today. Because payments grow at g while discounting works at r, each later payment's present value shrinks by the factor (1 + g) ÷ (1 + r) per period. Summing this geometric series gives the formula. When the payments go on forever and r > g, the series converges to P ÷ (r − g), the Gordon growth formula. Rate and growth must be for the same period length.

Worked example

Default inputs: first payment $10,000, growth 3%, rate 6%, 20 payments at the end of each period.

Ratio (1.03 ÷ 1.06)²⁰ ≈ 0.5632.
PV = 10,000 ÷ 0.03 × (1 − 0.5632) ≈ $145,615.33.
Future value = 145,615.33 × 1.06²⁰ ≈ $467,008.08.
Sum of payments = 10,000 × (1.03²⁰ − 1) ÷ 0.03 ≈ $268,703.74; last payment ≈ $17,535.06.
Total payments − PV ≈ $123,088.42; growing perpetuity = 10,000 ÷ 0.03 ≈ $333,333.33.

Each point is the calculator re-run with only “First payment” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

First payment	Present value
2,500	$36,403.83
5,000	$72,807.66
7,500	$109,211.49
10,000	$145,615.33
12,500	$182,019.16
15,000	$218,422.99
20,000	$291,230.65

How to read the result

The present value is the lump sum today that is equivalent to the whole stream at your rate. It is much less than the sum of payments because later payments are discounted. The perpetuity value shows the upper limit if the stream never ended. Higher growth or a lower rate raises the present value.

Common mistakes

Using a yearly rate with monthly payments.
Using the perpetuity formula when r ≤ g, where it does not apply.
Forgetting to multiply by (1 + r) for payments at the start of each period.
Confusing the first payment with today's value.

Keep in mind: Results depend on the chosen rate and growth, which are assumptions. This is not financial advice.

Frequently asked questions

What is a growing annuity?

A finite series of payments that increase by a constant percentage each period.

What happens if growth equals the discount rate?

Each payment's present value is the same, so PV = N × P ÷ (1 + r).

What is a growing perpetuity?

A growing annuity that never ends; its value is P ÷ (r − g) when r > g.

Sources: Present value of a growing annuity and growing perpetuity (standard time-value-of-money formulas)

Checked 9 Nov 2026. Present value of a growing annuity and growing perpetuity, annuity-due adjustment: standard time-value-of-money formulas.

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