Total return over the period
150.0%
Enter any beginning value, ending value and holding period to get the compound annual growth rate — the single annual rate that would have taken you from the first figure to the second. Then see how long that rate takes to double, triple or multiply your money by ten.
The holding period can be fractional; enter 3.5 for three and a half years. A negative growth rate produces no doubling time, and a rate of zero or below returns no multiple, because doubling never occurs.
| Multiple | Years required |
|---|---|
| 2× | 6.1 years |
| 3× | 9.6 years |
| 4× | 12.1 years |
| 5× | 14.1 years |
| 10× | 20.1 years |
The compound annual growth rate is the constant annual rate that would take the beginning value to the ending value over the stated period, assuming the value grew at that rate every year without deviation. It is the geometric mean of the annual returns, and it is a summary rather than a description.
On the default figures, $10,000 growing to $25,000 over eight years gives a multiple of 2.5, a total return of 150%, and a CAGR of 12.14%. Those three numbers describe the same event and answer different questions: 150% is the whole journey, 12.14% is the equivalent steady annual pace, and 2.5 is the scale factor that multiplies the starting amount.
The problem with CAGR is not that it is wrong. It is that it is smooth, and real sequences are not. Two funds can report the same compound annual growth rate while delivering completely different experiences to the people holding them.
The clearest illustration uses the arithmetic mean, which is the figure most often quoted alongside a fund's performance. Take a fund that rises 100% in year one and falls 50% in year two. The arithmetic average return is 25% a year, which sounds excellent. The actual outcome is that $1 becomes $2 and then $1: a total return of 0% and a CAGR of 0%. The 25% figure is technically the average of the two annual returns and it describes a fund that made nobody any money.
That gap between average and compound return is sometimes called volatility drag, and it is one of the few places where arithmetic produces a genuinely counter-intuitive result. The reason it happens is that a loss is applied to a smaller base than the gain that preceded it, so the two operations are not symmetric. A 50% loss requires a 100% gain to recover, and no averaging of the two disguises that.
The same asymmetry explains why a quoted total return is meaningless without its period. A 150% total return is excellent over eight years and unremarkable over thirty. It is also why the phrase "24% over three years" is ambiguous: it could mean a total return of 24%, which is 7.43% a year, or a 24% annual rate, which is a 90.6% total. Whenever a performance figure is quoted without stating whether it is cumulative or annualised, the first question to ask is which one it is.
The doubling table below the calculator is the most practical output here, because it converts a rate into a time horizon that is easy to reason about. At the default 12.14%, money doubles in 6.05 years, triples in 9.59, and multiplies tenfold in 20.10.
| Multiple | Years required at 12.14% | Years required at 7% | Years required at 3% |
|---|---|---|---|
| 2× | 6.05 | 10.24 | 23.45 |
| 3× | 9.59 | 16.24 | 37.17 |
| 4× | 12.10 | 20.49 | 46.90 |
| 5× | 14.05 | 23.79 | 54.45 |
| 10× | 20.10 | 34.03 | 77.90 |
The table also shows why the rule of 72 is useful and slightly imprecise. The rule says to divide 72 by the percentage rate to get the doubling time: at 12.14% that gives 5.93 years against the true 6.05, and at 3% it gives 24 years against the true 23.45. It is a good mental approximation and it drifts in a predictable direction at higher rates, which is exactly the behaviour of a shortcut rather than a formula.
The most important caveat about using a historical CAGR as a forward estimate is that the past rate was produced by a specific sequence of events that will not repeat. The number is a measurement of what happened, and the compound interest calculator is the right tool for turning an assumption about the future into a projection — with the assumption stated openly rather than inferred from history.
There is no universal answer, because the comparison that matters is against the risk taken and against alternative uses of the same money. What arithmetic can establish is that the figure is a rate of growth per year, not a total gain, so 10% CAGR over 20 years multiplies your money by 6.7 while 10% over 5 years multiplies it by 1.6. A useful discipline is to state the period alongside the rate every time you use the number, including when you are the one quoting it.
Usually because the quoted figure is a time-weighted or money-weighted return calculated on a different basis, or because it covers a different period, or because distributions were reinvested in one calculation and not the other. When you compute CAGR here from a beginning and ending value, you are assuming no contributions and no withdrawals, which is the cleanest case. If you added money along the way, your personal return will differ from the fund's and neither number is wrong.
CAGR, whenever the question is what actually happened to your money. The average of the annual returns overstates outcomes whenever returns vary, because it ignores the asymmetry between gains and losses. A fund that gains 100% and then loses 50% has an average annual return of 25% and a CAGR of 0%. The CAGR is the truthful one; the average is the flattering one.
No, and this is its main weakness as a comparison tool. Two investments with the same CAGR over the same period can have wildly different volatility, and the smoother one is preferable because it was easier to hold and less likely to have been abandoned at the worst moment. CAGR also says nothing about the maximum drawdown experienced along the way, which is the number that determines whether an investor stays invested.
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Cluster us/investing · Unit us-cagr-calculator · Engine compound-growth / cagr · Method: CAGR is the geometric mean annual rate: ending value divided by beginning value, raised to the power of one over the number of years, minus one.