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What Is CAGR?
Understanding the method
CAGR is useful for comparing growth over different durations when there are no intervening contributions or withdrawals. It says nothing about volatility or the return in a specific year. A positive final gain may include long periods of loss. If you add money during the period, treating the ending balance as investment growth overstates the result; use dated cash-flow analysis instead.
Worked example
₹1,00,000 growing to ₹2,00,000 over five years has CAGR of about 14.8698%. The total gain is 100%, but dividing 100% by five does not produce the compounded annual rate.
Formula and definitions
CAGR = [(final value / initial value)^(1 / years) − 1] × 100. Both values and duration must be positive.
How to use FinBizTools
- Record starting value and its date.
- Record ending value and valuation date, excluding unrelated assets.
- Enter the duration in years in the CAGR Calculator.
- If deposits or withdrawals occurred, move to XIRR and enter each actual date.
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Common mistakes and limitations
The tool supports fractional years but does not choose a day-count convention for you. A zero or negative initial/final value is outside this CAGR definition. CAGR is historical arithmetic, not a prediction.
Step-by-step CAGR calculation
Suppose an investment was worth ₹2,50,000 at the start and ₹4,10,000 exactly four years later, with no money added or withdrawn in between. The calculation has three steps.
- Divide the final value by the starting value. ₹4,10,000 ÷ ₹2,50,000 = 1.64. The investment grew to 1.64 times its original size.
- Raise the result to the power of one divided by the number of years. 1.64^(1/4) = 1.1316. This is the growth factor for one average year.
- Subtract one and convert to a percentage. 1.1316 − 1 = 0.1316, or a CAGR of about 13.16% per year.
You can check the answer by working forwards: ₹2,50,000 × 1.1316 × 1.1316 × 1.1316 × 1.1316 returns to roughly ₹4,10,000. The total gain was 64%, but 64% divided by four (16%) overstates the annual rate because it ignores compounding.
Periods that are not whole years
CAGR works with fractional years. Convert months to years by dividing by 12. If ₹1,00,000 became ₹1,50,000 over 42 months, the duration is 3.5 years and the CAGR is 1.5^(1/3.5) − 1, or about 12.28%. For dates that do not fall neatly on month-ends, count the days and divide by 365. The CAGR Calculator accepts decimal durations, so you can enter 3.5 or 2.75 directly.
Negative CAGR and losses
When the final value is below the starting value, CAGR is negative. ₹2,00,000 falling to ₹1,50,000 over three years is a total loss of 25%, which corresponds to a CAGR of about −9.14% per year. Again, dividing the total by the number of years (−8.33%) gives a different and incorrect figure.
Why CAGR differs from an average return
An arithmetic average of yearly returns can be very misleading when returns swing. Imagine ₹1,00,000 that gains 50% in year one (to ₹1,50,000) and loses 50% in year two (to ₹75,000). The average of +50% and −50% is 0%, yet the investor lost a quarter of the money. CAGR captures the actual outcome: (75,000 ÷ 1,00,000)^(1/2) − 1 = about −13.40% per year. This is why fund factsheets and company reports quote CAGR rather than an average of annual returns when they describe multi-year growth.
Comparing two investments with CAGR
CAGR is most useful when two outcomes cover different lengths of time. Investment A grew from ₹1,00,000 to ₹1,80,000 in five years; investment B grew from ₹1,00,000 to ₹1,50,000 in three years. A has the larger total gain (80% against 50%), but B grew faster: A’s CAGR is about 12.47% while B’s is about 14.47%. Whether B was the better choice still depends on risk, costs, taxes and whether the faster rate could have continued.
Adjusting CAGR for inflation
A nominal CAGR includes the effect of rising prices. To estimate a real growth rate, divide one plus the nominal rate by one plus the inflation rate and subtract one. With a nominal CAGR of 12% and inflation of 6%, the real rate is 1.12 ÷ 1.06 − 1, or about 5.66% per year, not the 6% you get by simple subtraction. The Inflation Calculator can show how much purchasing power a future amount represents.
A quick doubling check: the rule of 72
Dividing 72 by an annual growth rate gives a rough number of years for money to double. At 12% the rule suggests six years; the exact figure is about 6.12 years. The shortcut is handy for sanity-checking a CAGR result but becomes less accurate at very high or very low rates.
When to use CAGR, XIRR or absolute return
- Absolute return answers “how much did it grow in total?” and is fine for periods under a year.
- CAGR answers “what steady yearly rate links the start and end values?” when there is one starting amount and no further cash flows.
- XIRR is needed when money went in or came out on different dates, such as SIP instalments, top-ups or partial withdrawals.
Frequently asked questions
Can CAGR be negative?
Yes. A positive final value below the positive initial value produces a negative CAGR.
Disclaimer
This guide is educational. Examples are illustrative, not financial, tax or legal advice. Verify important decisions and current requirements. Read the FinBizTools Disclaimer.