What is the future value of a growing annuity formula?

FV = P1 × [(1 + r)n − (1 + g)n] ÷ (r − g), where P1 is the first deposit, r the interest rate, g the growth of the deposits and n the number of deposits.

How does it relate to the present value version?

FV = PV × (1 + r)n. Compounding the present value of the growing annuity forward n periods gives the same result.

Use FV = n × P1 × (1 + r)n−1. The calculator switches to it automatically.

Are deposits at the start or end of each period?

At the end. For start-of-period deposits multiply the result by (1 + r).

Future Value of Growing Annuity Formula

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Future Value of a Growing Annuity Calculator

Most people do not save the same amount for decades; contributions rise with pay. The future value of a growing annuity handles that case: the first deposit is P₁, each later deposit is g percent larger than the one before, and all of them earn r per period until the final deposit is made. The closed form is P₁ × [(1 + r)ⁿ − (1 + g)ⁿ] ÷ (r − g).

Formula

FV = P₁ × (1 + r)ⁿ − (1 + g)ⁿr − g

Where

FV: future value at the end of period n
P₁: first payment, at the end of period 1
r: interest (discount) rate per period
g: growth rate of the payment per period
n: number of payments

Calculator

First payment (P₁)

Rate per period (r) (%)

Growth rate (g) (%)

Number of payments (n)

Result and step-by-step solution

Future value of the growing annuity

366,348.80

Payments grow from 5,000.00 to 10,163.97 over 25 periods.

Convert the rates
r = 0.06, g = 0.03, n = 25
Compound both rates
(1 + r)ⁿ = 4.291871, (1 + g)ⁿ = 2.093778
Apply the formula
FV = 5,000.00 × 4.291871 − 2.0937780.03 = 366,348.80

How to use the formula

The calculator shows both compound factors, (1 + r)ⁿ and (1 + g)ⁿ, before dividing by the spread r − g. If r and g are equal the expression becomes 0 ÷ 0, so the special case n × P₁ × (1 + r)^{n − 1} is used instead.

The default case saves 5,000 in the first year, increases the contribution by 3% a year for 25 years and earns 6% a year: the account reaches 366,348.80. The final contribution is 10,163.97, so the plan roughly doubles the deposit over its life. Compare with a flat contribution using the future value of an annuity, or discount the same stream to today with the present value of a growing annuity.

Frequently asked questions

What is the future value of a growing annuity formula?: FV = P₁ × [(1 + r)ⁿ − (1 + g)ⁿ] ÷ (r − g), where P₁ is the first deposit, r the interest rate, g the growth of the deposits and n the number of deposits.
How does it relate to the present value version?: FV = PV × (1 + r)ⁿ. Compounding the present value of the growing annuity forward n periods gives the same result.
What if r equals g?: Use FV = n × P₁ × (1 + r)ⁿ⁻¹. The calculator switches to it automatically.
Are deposits at the start or end of each period?: At the end. For start-of-period deposits multiply the result by (1 + r).

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.