Annual CAGR: Measure Compounded Growth Between Two Values

Define the annual rate being measured

Compound annual growth rate, or CAGR, is the constant annual rate that connects a starting value with an ending value over a stated number of years. It smooths the change into an equivalent compounded path. It does not say that the actual value rose by that rate every year. Record the start and end dates before calculating, and use the same valuation basis at each end. A comparison of an account balance before a new deposit with a balance after that deposit does not isolate investment growth.

Derive the formula from compounded growth

If B is the beginning value, E the ending value and n the elapsed years, then E=B×(1+r)^n for the equivalent constant rate r. Divide by B, take the nth root and subtract one: r=(E/B)^(1/n)−1. Multiply r by 100 for a percentage. The linked calculator requires a positive beginning value and a positive elapsed period. Its ending value can be zero or positive. Do not enter an initial negative cash outflow as B; this endpoint calculation uses asset values rather than an IRR cash-flow schedule.

Check a five-year example

Suppose a value grows from 10,000 to 15,000 over exactly five years without outside deposits or withdrawals. The growth factor is 1.5, and the fifth root is approximately 1.084471771. Subtracting one gives annual CAGR of approximately 8.447177%, displayed by the tool as 8.4472%. Total growth is 50%. Dividing 50% by five gives 10%, but that is a simple average of total growth and does not reproduce the ending value when compounded. Verify the result by calculating 10,000×(1.084471771)^5, which returns approximately 15,000.

Compare geometric and arithmetic averages

Consider annual returns of +20% and −10%. An initial 100 becomes 120 and then 108. The two-year growth factor is 1.2×0.9=1.08, giving CAGR of sqrt(1.08)−1, approximately 3.92305% per year. The arithmetic mean is (20%−10%)/2=5%. These figures answer different questions: 3.92305% reproduces the compounded endpoint, while 5% is the mean of the two listed annual percentage returns. Enter 100, 108 and 2 in the calculator to check the compounded measure without confusing the two definitions.

Handle decreases and the zero boundary

A value falling from 10,000 to 8,000 over two years has CAGR sqrt(0.8)−1, approximately −10.55728%. A negative result is a valid description of declining positive values. If the ending value is zero, the endpoint formula returns −100%. A zero beginning value makes the ratio undefined, and a negative ending value does not fit the ordinary positive-value growth interpretation used here. For business figures that cross zero, report the actual amounts and changes rather than forcing them into a conventional CAGR calculation.

Keep external cash flows out of the endpoint shortcut

If an account starts at 10,000, receives a 5,000 deposit and ends at 15,000, the apparent endpoint growth could be entirely new money. Applying the five-year example's CAGR to that account would mislabel the deposit as return. Cash-flow timing calls for a suitable money-weighted calculation, or for a time-weighted method that separates periods around external flows. Income distributions also need consistent treatment: an ending market value that excludes dividends differs from a total-return value with reinvestment. State which version is being measured and whether fees are included.

Choose dates and precision deliberately

The calculator accepts a number of years, not two dates. For a period that is not a whole number of years, determine the fractional-year convention first and use it consistently. Eighteen months represented as 1.5 years is a reasonable explicit monthly convention, but an exact dated calculation may use a specified day-count basis. Keep full values through the calculation and round only the reported rate. CAGR summarizes the endpoints; it hides volatility, drawdowns and the sequence of interim returns, so retain that history when evaluating the experience of holding the asset.

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