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Exponential Growth

A=A0(1+r)tA = A_0 (1 + r)^{t}
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Worked example: 1000 at 5% for 10 periods → 1628.8946. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

See also

Exponential Decay: Both use final amount and initial amount.Exponential Growth by Doubling Time: Both use final amount and initial amount.Compound Interest (Periodic): Both use number of periods.Continuous Compounding: Both use number of periods.Present Value: Both use number of periods.Simple Interest: Both use number of periods.
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Exponential Growth explained

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Anything that grows by a fixed percentage each period (money at compound interest, populations, subscriber counts) multiplies by (1 + r) every step, so growth compounds on itself. Enter r as a decimal: 5% is 0.05. Worked example: $1,000 invested at 5% per year for 10 years gives A = 1000 × 1.05¹⁰ ≈ $1,628.89. The extra $128.89 beyond simple interest is interest earned on earlier interest. Einstein may never have called compound interest the eighth wonder of the world, but bankers behave as if he did.

The same formula runs backward. Solving for r extracts an average per-period growth rate from two snapshots, and solving for t (using logarithms) answers "how long until we reach A?" A handy shortcut, the Rule of 72, falls straight out of the t rearrangement: dividing 72 by the percentage rate approximates the doubling time, so money at 6% doubles in roughly 12 years.

Exponential Growth formula

A=A0(1+r)tA = A_0 (1 + r)^{t}
Where
  • AA= Final amount
  • A0A_0= Initial amount
  • rr= Growth rate per period (decimal)
  • tt= Number of periods
Revised 31 October 2026
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formula.expert. (2026, October 31). Exponential Growth Formula & Calculator. https://formula.expert/solvers/exponential-growth

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