Compound Growth Calculator Formula

Understand the math behind the compound growth calculator. Each variable explained with a worked example.

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Formulas Used

CAGR (%)

cagr = (pow(final_val / initial, 1 / periods) - 1) * 100

Total Growth Factor

growth_factor = final_val / initial

Total Return (%)

total_return = ((final_val - initial) / initial) * 100

Variables

VariableDescriptionDefault
initialInitial Value1000
final_valFinal Value2000
periodsNumber of Periods5

How It Works

How to Calculate Compound Annual Growth Rate

Formula

CAGR = (Final / Initial)^(1/n) - 1

CAGR is the constant annual growth rate that would take the initial value to the final value over n periods. It smooths out volatility and gives a single rate that represents the equivalent steady growth. Multiply by 100 to express as a percentage.

Worked Example

An investment grows from $1,000 to $2,000 over 5 years.

initial = 1000final_val = 2000periods = 5
  1. 01Growth factor = 2000 / 1000 = 2.0
  2. 02CAGR = 2.0^(1/5) - 1 = 2.0^0.2 - 1
  3. 03= 1.14870 - 1 = 0.14870
  4. 04CAGR = 14.87% per year
  5. 05Total return = 100%

Frequently Asked Questions

Why use CAGR instead of average growth?

Simple average of yearly growth rates does not account for compounding and can be misleading. CAGR gives the actual equivalent growth rate that produces the observed result. For example, +100% then -50% has average growth of 25% but CAGR of 0%.

Does CAGR reflect actual year-by-year performance?

No. CAGR assumes smooth, constant growth. The actual path may have been volatile. CAGR is useful for comparing investments over the same period but hides interim volatility.

Can CAGR be negative?

Yes. If the final value is less than the initial value, CAGR will be negative, indicating compound decline over the period.

Ready to run the numbers?

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