Growing Annuity Calculator
A growing annuity is a series of periodic payments that increase by a fixed percentage each period. Enter the first payment, discount rate, growth rate, and number of periods to find the present value or future value instantly. Switch the solve mode to work backward from a target lump sum to the required first payment. A full payment schedule and balance growth chart update as you type.
Formula
Worked example
An employee saves $5,000 in year 1 and increases contributions by 3% each year for 20 years. The account earns 7% annually. PV = 5000 / (0.07 - 0.03) * [1 - (1.03/1.07)^20] = 5000 / 0.04 * [1 - 0.4564] = 125,000 * 0.5436 = $67,950. FV = 5000 * [(1.07^20) - (1.03^20)] / (0.07 - 0.03) = 5000 * [3.8697 - 1.8061] / 0.04 = $257,952.
What is a growing annuity?
A growing annuity is a finite stream of cash flows where each payment is larger than the last by a fixed percentage called the growth rate. Unlike a regular annuity with level payments, the amounts escalate each period, making this model ideal for salary-linked retirement savings, rent escalation clauses, dividend growth stocks, and any other contract where payments rise with inflation or income growth. The two key time-value outputs are the present value (what the entire stream is worth as a lump sum today) and the future value (what all the payments grow to if reinvested at the stated return). When the growth rate equals zero, the formulas reduce to the standard level-annuity formulas.
Present value formula and how to read it
The present value of a growing ordinary annuity is PV = P / (r - g) * [1 - ((1+g)/(1+r))^n], where P is the first payment, r is the periodic discount rate, g is the periodic growth rate, and n is the number of periods. The term P / (r - g) is the Gordon Growth Model for a perpetuity; the bracket [1 - ((1+g)/(1+r))^n] scales it down to a finite horizon. When r and g are equal, the formula has a zero denominator and the limit simplifies to PV = P * n / (1 + r). For an annuity due (payments at the start of each period) multiply by (1 + r) to account for the one-period head start. The present value rises as g approaches r from below, because later payments are relatively larger and the discounting headwind weakens.
Future value and the accumulation picture
Future value answers a different question: if you deposit each growing payment into an account earning the stated rate, how much do you have at the end? The formula is FV = P * [(1+r)^n - (1+g)^n] / (r - g). You can verify it by noting that FV = PV * (1+r)^n. The gap between total cash paid and the future value is pure investment return: the compounding effect. A payment schedule computed period by period lets you see exactly how the balance and cumulative deposits diverge over time.
Ordinary annuity vs. annuity due
An ordinary annuity (the default) makes each payment at the END of the period. An annuity due makes each payment at the START, meaning every deposit earns one extra period of interest. As a result, the PV and FV of an annuity due are each exactly (1 + r) times the ordinary equivalent. Most employee savings plans and mortgages use the ordinary-annuity convention; lease agreements and insurance premiums often use the annuity-due convention. The calculator lets you toggle between them; check your contract to confirm which applies.
Example growing annuity scenarios
| Growth rate | Present value | Future value | Total cash paid | Context |
|---|---|---|---|---|
| 0% | $53,023 | $205,325 | $100,000 | Flat ordinary annuity (baseline) |
| 2% | $62,469 | $242,089 | $121,899 | Inflation-indexed pension |
| 3% | $68,212 | $264,098 | $134,352 | Salary-linked 401(k) saving |
| 5% | $83,036 | $322,097 | $165,330 | Rapidly growing dividend stream |
| 7% | $100,000 | $386,968 | $204,977 | Growth rate equals discount rate |
Present and future values for a $5,000 first payment over 20 years at a 7% discount rate with various growth rates.
Frequently asked questions
What happens when the growth rate equals the discount rate?
The standard PV formula divides by (r - g), which becomes zero when r = g. In that limit the formula is replaced by PV = P * n / (1 + r) and FV = P * n * (1+r)^(n-1). This calculator detects that condition automatically and switches to the limit formula so you never see a division-by-zero error.
What is the difference between a growing annuity and a growing perpetuity?
A growing perpetuity has no end date: payments continue forever. Its PV is simply P / (r - g), provided r > g. A growing annuity adds a finite horizon n, which scales down the perpetuity value by the bracket [1 - ((1+g)/(1+r))^n]. As n approaches infinity the bracket approaches 1 and the annuity value converges to the perpetuity value.
Can I use a monthly growth rate and discount rate?
Yes. Set the period count to the number of months, enter the monthly discount rate (annual rate divided by 12 as a first approximation, or the exact effective monthly rate), and the monthly growth rate. For example, for annual rates of 7% and 3% with monthly periods, use r = 7/12 % per month and g = 3/12 % per month, or convert using the effective monthly formula (1 + annual rate)^(1/12) - 1.
What does "solve for first payment" mode do?
Instead of computing PV or FV from a known first payment, this mode works backward. You supply a target present value or future value and the calculator divides it by the unit annuity factor to find the first-period payment that produces exactly that target. This is useful when you know, for example, that you need $500,000 at retirement (FV) and want to find the starting contribution for a salary-escalating savings plan.
How do I use this for salary-linked retirement savings?
Set the first payment to your planned first-year contribution, the growth rate to your expected annual salary increase, the discount rate to your expected portfolio return, and the number of periods to the years until retirement. The future value is the projected balance at retirement assuming you invest each growing contribution at the start of its year. The payment schedule shows how each annual deposit and the running balance evolve.
Does a negative growth rate work?
Yes. A negative growth rate models payments that shrink each period, for example a declining royalty stream or a fixed nominal payment eroded by deflation. The same formulas apply; just enter a negative percentage. The only constraint is that r must still be positive for the present value to be finite.