Compound Annual Growth Rate (CAGR)

The single annual rate that would take a beginning value to an ending value over n years with annual compounding. It smooths a lumpy path into one comparable growth figure.

When to use: Use to compare investments, revenues or any quantity that grew over different periods on one annualized basis. It is the same calculation as solving a lump sum for its rate.

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Formula

CAGR = \left(\frac{V_{\text{end}}}{V_{\text{begin}}}\right)^{1/n} - 1

Variables

Symbol	Name	Description	Unit
CAGR	CAGR	Annualized growth rate	%
BeginValue	Beginning Value	Value at the start of the period	$
EndValue	Ending Value	Value at the end of the period	$
n	Number of Years	Investment time horizon in years	years

Real-Life Examples

Example 1: Portfolio Over a Decade

A portfolio grew from $10,000 to $25,000 in 10 years.

Given

BeginValue = $10,000.00EndValue = $25,000.00n = 10.00 years

Step-by-Step

1.Growth multiple = 25,000 / 10,000 = 2.5

2.CAGR = 2.5^(1/10) − 1

3.CAGR = 9.5958%

Result:9.5958%

The portfolio grew as if it had earned a steady 9.6% a year, whatever the year-to-year path actually was.

Example 2: A Decline

Revenue fell from $50,000 to $42,000 over 3 years.

Given

BeginValue = $50,000.00EndValue = $42,000.00n = 3.00 years

Step-by-Step

1.Growth multiple = 42,000 / 50,000 = 0.84

2.CAGR = 0.84^(1/3) − 1

3.CAGR = -5.6461%

Result:-5.6461%

A negative CAGR: revenue shrank at an annualized 5.6%. The formula handles declines as naturally as growth.

Frequently Asked Questions

The arithmetic average of yearly returns overstates growth when returns vary. CAGR is the geometric rate that actually reproduces the ending value, so it is the honest comparison figure.

Yes. Solving a lump sum for its annual rate given PV, FV and n is exactly this formula with different variable names.

Related Formulas

Lump Sum

Same family

Geometric Mean Return

Discount Factor Rule of 72 (Doubling Time)