Growing annuity

A growing annuity is a finite series of cash flows that increases at a constant rate g each period for n periods. Its present value uses a closed-form formula that reduces to a plain annuity when g equals zero.

ByHoang TruongUpdated July 2, 2026

FrameworkTime value of money

See it move

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A project pays €80,000 at the end of year one, then grows 4% annually for five years: €83,200, €86,528, €89,989 and €93,588 in the final year. Discounted at a 10% cost of capital, the growing-annuity formula values this finite, growing stream today at approximately €330,000.

Where it fits

TopicTime Value of MoneyAdvancedSubjectCorporate FinanceAdvanced

The formula

LaTeX

PV = \frac{C_1}{r - g} \left[1 - \left(\frac{1 + g}{1 + r}\right)^n\right]

Variables

$P V$: Present value of the growing annuity
$C_{1}$: Cash flow received at the end of period one
$r$: Discount rate per period
$g$: Constant growth rate per period
$n$: Number of periods

When g = 0 the formula reduces to the standard annuity: C ÷ r × [1 − (1 + r)^(−n)]. When r = g exactly, PV = n × C₁ ÷ (1 + r).