Exponential Growth

A = A_0 (1 + r)^{t}

A =

A₀ =

r =

t =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

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

A = A_0 (1 + r)^{t}

Where

$A$ = Final amount
$A_0$ = Initial amount
$r$ = Growth rate per period (decimal)
$t$ = Number of periods

Missing one of these? Work it out first, then come back

Final amount — Exponential Decay, Exponential Growth by Doubling Time
Initial amount — Exponential Decay, Exponential Growth by Doubling Time
Growth rate per period (decimal) — Exponential Decay, Simple Interest
Number of periods — Exponential Decay, Simple Interest