Growing Annuity Calculator
Value a fixed-term stream of payments that grow each period — the present value of a growing annuity.
How it works
PV = C ÷ (r − g) × [ 1 − ((1 + g) ÷ (1 + r))ⁿ ] · when r = g: PV = n × C ÷ (1 + r)
A growing annuity pays for a fixed number of periods, but each payment is larger than the last by a constant growth rate — think of a pension with cost-of-living rises or a lease with annual escalations. Its present value blends the ordinary annuity formula with a growth term; when the discount rate happens to equal the growth rate the general formula divides by zero, so a separate limiting case is used. Unlike a perpetuity, it is always finite because it ends after n payments.
Worked example
Twenty annual payments starting at $1,000 and rising 3% a year, discounted at 8%, are worth 1,000 ÷ (0.08 − 0.03) × [1 − (1.03 ÷ 1.08)^20] = 20,000 × (1 − 0.3874) = about $12,252. The final payment has grown to roughly $1,754 by year 20.
Frequently asked questions
How is a growing annuity different from a growing perpetuity?
A growing annuity stops after a set number of payments, while a growing perpetuity continues forever. The annuity formula subtracts a term that removes all payments beyond year n.
What happens when the growth rate equals the discount rate?
The standard formula divides by (r − g), which becomes zero. In that case every discounted payment is equal, so the present value is simply n payments discounted one period: n × C ÷ (1 + r).
Where are growing annuities used?
They model inflation-linked pensions, escalating leases, and salary or dividend streams that rise at a steady percentage each period for a limited time.
Related calculators
Educational estimate, not investment advice.