Growing Annuity Calculator

Free Growing Annuity Calculator

This growing annuity calculator works out the present value of a series of payments that increase by a fixed percentage every period, instead of staying flat like a regular annuity. You enter the first payment, how fast it grows each period, a discount rate, and how many years the payments continue. The calculator instantly returns the present value — what that entire growing payment stream is worth in today's money — along with the future value, a full period-by-period chart, and a downloadable breakdown table.

A growing annuity shows up more often than people realize. A salary that gets a yearly raise, a lease payment that increases with inflation, a dividend that grows every year, a pension that adjusts for cost-of-living — all of these are, mathematically, growing annuities. This calculator also includes an advanced growing perpetuity mode for the special case where the payments are expected to keep growing forever, plus support for both ordinary annuities (payment at the end of each period) and annuities due (payment at the start of each period).

What Is a Growing Annuity?

A growing annuity is a series of periodic payments where each payment is larger than the one before it, by a constant percentage growth rate. This is different from a regular (level) annuity, where every payment is exactly the same amount. Because later payments are worth more in nominal terms but also happen further in the future, working out the present value requires accounting for both the growth rate pushing payments up and the discount rate pulling their value back down to today.

Growing annuities are common in real financial situations: a salary or pension that increases every year, rental income that rises with a lease escalation clause, dividends from a stock that has a history of raising its payout, or any cash flow that's expected to grow at a steady percentage rather than stay flat.

Growing Annuity Present Value Formula

For an ordinary growing annuity, where the discount rate (r) is not equal to the growth rate (g), the present value formula is:

PV = [P₁ ÷ (r − g)] × [1 − ((1 + g) ÷ (1 + r))ⁿ]

• PV = the present value of the entire growing payment stream
• P₁ = the amount of the first payment
• r = the discount rate per period
• g = the growth rate per period
• n = the total number of payments

The Growing Perpetuity Formula

When the payments are expected to grow forever rather than stop after a set number of years, the formula simplifies dramatically, because the far-future terms shrink toward zero as long as the discount rate stays higher than the growth rate:

PV = P₁ ÷ (r − g)

This growing perpetuity formula only works when r is greater than g. If the growth rate is equal to or higher than the discount rate, the value never converges — mathematically, the payment stream would be worth an infinite amount, which isn't realistic. This calculator automatically disables the perpetuity mode whenever that condition isn't met, and sticks with the finite-term formula instead.

Ordinary Annuity vs. Annuity Due

The timing of each payment within its period changes the present value slightly. In an ordinary growing annuity, each payment happens at the end of the period — this is the standard assumption for most loans, bonds, and many annuity contracts. In a growing annuity due, each payment happens at the start of the period instead, which is typical for things like lease payments and insurance premiums paid in advance. Because an annuity due's payments arrive slightly earlier, its present value is always a bit higher than an otherwise identical ordinary annuity — specifically, exactly (1 + r) times higher. This calculator lets you switch between the two so you're using the timing that actually matches your situation.

Worked Example — Growing Annuity Present Value

Say you're valuing a payment stream that starts at $10,000, grows by 3% every year, gets discounted at an 8% rate, and continues for 15 years.

• Growth rate: 3%, discount rate: 8%, so r − g = 5%.
• Plugging into the formula: PV = [10,000 ÷ 0.05] × [1 − (1.03 ÷ 1.08)¹⁵].
• That works out to roughly $109,000 in present value — meaningfully more than a flat, non-growing $10,000-a-year annuity over the same 15 years would be worth, purely because each payment is a little larger than the last.
• The final (15th) payment itself, after compounding 3% growth for 14 years, comes out to roughly $14,700 — nearly 50% larger than the first payment.

Why the Discount Rate Must Be Higher Than the Growth Rate

For a finite-term growing annuity, the math still works even if the growth rate is higher than the discount rate — the formula simply produces a larger present value the closer the two rates get, and it still resolves cleanly as long as the number of periods is finite. It's only in the perpetuity case, where payments continue forever, that growth needs to stay below the discount rate. Otherwise, each payment's growth would outrun the discounting applied to it, and the sum of an infinite series of ever-larger, ever-more-valuable payments would never settle on a finite number.

Growing Annuity vs. Regular (Level) Annuity

A regular annuity pays the exact same amount every period, so its present value only depends on the payment size, the discount rate, and the number of periods. A growing annuity adds one more moving part — the growth rate — which pushes each payment a little higher than the last. All else being equal, a growing annuity is always worth more than a level annuity using the same first payment, because later payments in the growing version are larger. This calculator can actually be used to model a level annuity too: simply set the growth rate to 0%, and the formula collapses to the standard ordinary annuity present value calculation.

Common Uses for Growing Annuity Calculations

This kind of present value calculation shows up across a wide range of financial planning and valuation situations. It's used to value a pension or salary stream that includes annual cost-of-living increases, to price a lease with a scheduled rent escalation, to estimate the fair value of a stock using a dividend discount model where dividends are assumed to grow every year, and to compare job offers or income streams that include built-in annual raises against flat-salary alternatives. Anywhere a cash flow grows by a steady percentage instead of staying level, this calculation applies.

Common Mistakes When Calculating Growing Annuities

A frequent mistake is applying the standard level-annuity formula to a payment stream that actually grows, which understates the true present value since it ignores the fact that later payments are larger. Another common error is mixing up the growth rate and the discount rate, or forgetting to convert an annual rate down to a per-period rate when payments happen more often than once a year. It's also easy to accidentally try to value a perpetuity where the growth rate is equal to or higher than the discount rate — a mathematically undefined case that this calculator flags automatically by disabling perpetuity mode when the condition isn't met.

Why Use This Growing Annuity Calculator?

This calculator works out the present value — and the future value — of a growing payment stream using the correct growing annuity formula, with support for both ordinary and annuity-due timing, an automatic growing perpetuity mode for infinite payment streams, and any payment frequency from annual to monthly. You get an instant present value, a full period-by-period chart showing how each nominal payment and its discounted value change over time, and a downloadable CSV breakdown — so whether you're valuing a growing pension, pricing an escalating lease, comparing salary offers with different raise schedules, or working through a finance course assignment, you get an accurate answer in seconds instead of working through the formula by hand.