π± Growing Annuity Calculator
Present value of rising payments.
Present value of the growing annuity
Estimates for planning only, not financial advice.
A growing annuity is a stream of payments that rises at a constant rate: the first payment is $12,000, each payment grows 3%, the discount rate is 7%, and it runs 20 periods. Its present value is $159,987, far above a flat annuity's value because the later payments keep swelling. Dividend growth stocks and rising pension payouts are growing annuities in the wild.
How to Use This Calculator
Enter the first payment, the discount rate, the per-period growth rate, and the number of payments. The calculator returns the present value and the undiscounted total for comparison.
Enter the first payment amount.
Enter the discount rate and the growth rate (growth must be lower).
Enter the number of periods and read the present value. For a flat payment stream, our present value calculator handles the classic case.
The Growing Annuity Formula
Each payment is discounted and grown simultaneously: payment t is PMT x (1+g)^(t-1) / (1+r)^t. Summing the geometric series gives the closed form above. The (r - g) denominator is the effective discount rate after growth, which is why the formula explodes as g approaches r: if payments grow as fast as you discount them, the present value is unbounded. Let n go to infinity and you get the Gordon growth model, the workhorse of stock valuation.
Worked Example
First payment $12,000, growth 3%, discount 7%, 20 payments. PV = 12,000 / 0.04 x [1 - (1.03/1.07)^20] = 300,000 x 0.5333 = $159,987. The undiscounted total of all 20 payments is about $406,300, so discounting at 7% erases more than half the nominal sum, yet the value still dwarfs a flat $12,000 annuity, whose PV at 7% is only $127,128. That $32,859 gap is the price of 3% growth, and it shows why growth assumptions dominate valuations.
Where Growing Annuities Hide
Dividend discount models are growing annuities with infinite horizons. Rising lease payments with contractual escalators are finite ones. Salary projections over a career are growing annuities too, useful for valuing pension promises or human capital. The danger is always the growth rate: a 5% assumption versus 3% can double the answer, and historical growth rarely persists. Cap perpetual growth near the economy's growth rate and stress-test everything above it.
My rule: use growing annuities for explicitly contracted or historically stable growth, never for hoped-for growth. The formula is honest; the input is where optimism sneaks in. When growth is uncertain, run the flat annuity alongside and treat the difference as the price of your optimism.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is a growing annuity?
A series of payments that increase at a constant rate each period, like dividends growing 5% a year. Its present value accounts for both the growth and the time value of money.
What is the growing annuity formula?
PV = PMT / (r - g) x [1 - ((1+g)/(1+r))^n], where PMT is the first payment, r the discount rate, g the growth rate, and n the number of periods. The discount rate must exceed the growth rate.
What happens if growth exceeds the discount rate?
The formula breaks: present value would be infinite, which is economically meaningless. It signals an impossible assumption, since no cash flow can grow faster than the discount rate forever.
Growing annuity vs growing perpetuity?
The annuity ends after n periods; the perpetuity runs forever and simplifies to PMT / (r - g). The perpetuity version is the Gordon growth model used in stock valuation.
How do dividends fit this model?
A dividend growing at a steady rate is a growing perpetuity in theory. Analysts use multi-stage models in practice: high growth for some years, then a stable rate, because no company grows fast forever.
Can growth be negative?
Yes, a shrinking payment stream, like a declining royalty. The formula handles negative g fine, and the present value falls below the flat annuity case, as intuition suggests.
Why is the PV so sensitive to g?
Because growth compounds inside the discount factor every period. A two-point change in g can move the answer 30% or more, which is why growth assumptions deserve the most scrutiny in any valuation.
When should I use a flat annuity instead?
For fixed payments like mortgages, bonds, and leases without escalators. Use the growing version only when payments genuinely rise contractually or with strong historical evidence.
How do I value a growing annuity with uneven growth?
Split it into stages: project the high-growth years individually, then apply the growing-annuity formula from the stable year onward and discount that value back. Multi-stage DCFs are just chained applications of this formula.
What discount rate fits a growing annuity?
The opportunity cost of similar-risk cash flows: WACC for firm cash flows, cost of equity for equity cash flows, or your personal hurdle rate. The rate must exceed growth, and riskier streams deserve higher rates.