Growing Annuity Calculator — PV & FV
Find the present or future value of a series of payments that grow at a constant rate each period — useful for valuing dividend streams, rent escalations, salary-linked pensions and any escalating cash flow.
% per period
% per period
Lump sum today worth the same as all future growing payments
- 1
Discount ratio
(1 + 0.03) ÷ (1 + 0.07) = 0.962617Each payment grows by g but is discounted at r; this ratio captures both effects. - 2
Ratio raised to n
0.962617ⁿ (n = 20) = 0.466733 - 3
Bracket 1 − ratioⁿ
1 − 0.466733 = 0.533267 - 4
Present value
(1,000 ÷ (0.07 − 0.03)) × 0.533267 = 13,331.66
How does this calculator work?
A growing annuity pays PMT in period 1, then PMT × (1+g), PMT × (1+g)², … up to n periods. Its present value is PV = PMT / (r − g) × [1 − ((1+g)/(1+r))^n]. Enter first payment, discount rate, growth rate and number of periods for both PV and FV. When r = g use PMT × n / (1+r).
Formula
How this is calculated
A growing annuity (also called a growing ordinary annuity) is a finite series of cash flows where the first payment is PMT, and each subsequent payment grows by the factor (1 + g): the second payment is PMT × (1+g), the third PMT × (1+g)², and so on. The present value discounts each payment back to today using the periodic discount rate r.
When r ≠ g the present value collapses to the compact formula PV = PMT / (r − g) × [1 − ((1+g)/(1+r))^n]. If r = g the formula is undefined (division by zero) and the special case PV = PMT × n / (1+r) applies instead. The future value FV = PV × (1+r)^n is equivalently given by FV = PMT × [(1+r)^n − (1+g)^n] / (r−g). When n → ∞ and r > g the formula converges to the Gordon Growth Model used in stock valuation: PV = PMT / (r − g).
Both rates and the growth rate are per-period figures — if payments are annual, enter annual rates; if monthly, use monthly rates. The model assumes payments occur at the end of each period (ordinary annuity), constant rates throughout, and no mid-period compounding. Sensitivity to the growth rate is high: a small change in g produces a large change in PV, so treat results as estimates when g is close to r.
Frequently asked questions
The standard formula produces a zero denominator. The special case is PV = PMT × n / (1 + r), which still gives a finite result. This calculator switches to that formula automatically when r and g are within a rounding threshold of each other.
A regular (flat) annuity pays the same amount each period. A growing annuity pays an amount that increases by g% each period. When g = 0 the two formulas are identical. Growing annuities better model rent escalations, salary-linked pensions and dividend streams that grow with inflation or earnings.
Yes — a negative g means payments shrink each period, such as a declining royalty or a depleting asset. The same formula applies as long as g > −1 (payments remain positive) and r ≠ g.
Also known as
TG we-Calculate Editorial Team. (2026). Growing Annuity Calculator — PV & FV [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/growing-annuity-calculator
TG we-Calculate Editorial Team. "Growing Annuity Calculator — PV & FV." TG we-Calculate. 2026. https://we-calculate.com/calculator/growing-annuity-calculator.
TG we-Calculate Editorial Team, "Growing Annuity Calculator — PV & FV," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/growing-annuity-calculator
@misc{wecalculate_growing_annuity_calculator, title = {Growing Annuity Calculator — PV & FV}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/growing-annuity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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