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Constant Annual Exponential Growth & Decay

Project a positive quantity using a constant annual percentage rate, or solve for time, rate or starting value under the same model.

Calculator inputs

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Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

A starting quantity of 100 growing 10% per year becomes 121 after two years. At a −10% annual rate it becomes 81.

Final value = initial value × (1 + annual percentage rate / 100)^elapsed years

Enter these known values and leave the other values blank.

The percentage rate is per year, even when duration is displayed in seconds, months or another unit. This model uses a Julian year of 365.25 days and one twelfth of that year per month.
The rate stays constant, with no additions, removals, carrying capacity or other limits. Fractional years use a fractional exponent.
Initial and final quantities must be positive; the rate must exceed −100% and elapsed time cannot be negative. Negative rates represent decay.
At zero elapsed time the final value equals the initial value. At zero growth rate a time inferred from unchanged values is not uniquely determined.
Modeled counts may be fractional. Rounding to whole organisms or items is a separate decision, and this arithmetic does not predict real population behavior.

No. The percentage remains annual. The duration is converted to Julian years before applying the exponent.

Bookify requires positive initial and final quantities, an annual rate above −100% and nonnegative elapsed time for this real-valued growth model.