Exponential Growth Prediction Calculator

Project a future value from steady exponential growth. Enter a starting value, a growth rate per period, and the number of periods to get the predicted amount, total growth, and doubling time using A = P(1 + r)t.

Quick Facts

Formula
A = P(1 + r)t
Discrete exponential growth. Rate r is entered as a percent and used as a decimal; each period multiplies the value by (1 + r).

Your Results

Calculated
Predicted value
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A = P(1 + r)^t
Total growth
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Increase over the starting value
Growth multiple
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Final ÷ starting value
Doubling time
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Periods to double at this rate

Ready

Enter a starting value, growth rate, and number of periods, then calculate.

Understanding exponential growth prediction

Exponential growth happens when a quantity increases by a constant percentage each period rather than by a constant amount. Because each period's growth is applied to a larger base than the one before, the total accelerates over time. This calculator predicts the future value of such a quantity from three inputs: the starting value, the growth rate per period, and the number of periods.

The formula

The discrete exponential growth model is:

A = P(1 + r)t

  • A = predicted (future) value
  • P = starting value, P₀
  • r = growth rate per period as a decimal (enter 5 for 5%, which the tool converts to 0.05)
  • t = number of periods

Each period multiplies the running total by the factor (1 + r). Growing $1,000 at 5% per year for 10 years gives 1000 × 1.0510 ≈ $1,628.89. A negative rate models exponential decay: entering −10% shrinks the value by a factor of 0.9 each period.

Discrete vs. continuous growth

The formula above compounds once per period. When growth is truly continuous — compounded every instant — the model becomes A = P·ert, where e ≈ 2.71828. Continuous compounding always yields a slightly larger result for the same nominal rate: at r = 5% for one year, (1.05) = 1.05 versus e0.05 ≈ 1.05127. This calculator uses the discrete form, which matches how most real-world rates (annual interest, yearly population figures, per-round metrics) are quoted.

Doubling time and the Rule of 72

A hallmark of exponential growth is a fixed doubling time that does not depend on the starting value. The exact doubling time is t = ln(2) / ln(1 + r). The Rule of 72 is a fast mental estimate: divide 72 by the percent rate. At 6% per period the rule gives 72 ÷ 6 = 12 periods, while the exact value is ln(2)/ln(1.06) ≈ 11.90 periods — close enough for quick checks.

Common reference points

  • 7% ≈ doubles in ~10 periods (ln 2 / ln 1.07 ≈ 10.24). A long-run stock-market rule of thumb.
  • 2% ≈ doubles in ~35 periods (≈ 35.0). Typical of slow population or inflation growth.
  • 100% growth rate means the quantity doubles every single period (multiplier 2).
  • Bacterial growth is a classic case: a colony dividing every 20 minutes has r = 100% per 20-minute period.

Frequently Asked Questions

What formula does this exponential growth calculator use?
It uses the discrete exponential growth formula A = P(1 + r)t, where P is the starting value, r is the growth rate per period as a decimal, and t is the number of periods. For example, 1,000 growing at 5% per year for 10 years gives 1000 × 1.0510 ≈ 1,628.89.
How do I find the doubling time?
The exact doubling time is t = ln(2) / ln(1 + r). A quick estimate is the Rule of 72: divide 72 by the percent growth rate. At 6% per period, 72 ÷ 6 = 12 periods, while the exact value is ln(2)/ln(1.06) ≈ 11.90 periods.
Can I model decay instead of growth?
Yes. Enter a negative growth rate. For example, −10% per period multiplies the value by 0.9 each period, so 1,000 becomes 1000 × 0.95 ≈ 590.49 after 5 periods. The calculator reports how many periods it takes the value to halve.
Does the period have to be years?
No. A period can be any consistent time step — years, months, days, or event rounds — as long as the growth rate is expressed per that same period. Just make sure t and r use the same unit. To convert an annual rate to a monthly one, use (1 + annual)1/12 − 1 rather than dividing by 12.

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