What Is CAGR? How to Calculate Annual Growth

Every investing pitch quotes growth, and almost none of them define the measure they are quoting. One page says a holding gained 96 percent, another says it returned 7 percent a year, a third says it averaged 10 percent, and all three can describe the same money. The number that resolves the confusion is the compound annual growth rate, usually written as CAGR, because it converts any result over any length of time into a single comparable speed. It is the closest thing investing has to a common unit, and it takes about two minutes to learn.

This breakdown works CAGR from the ground up: the formula written out in plain words, a full calculation you can follow with a pencil, why it is a geometric mean rather than a plain average, and the exact reason the plain average flatters results that a real investor never received. It also covers what the smooth number quietly hides, why the order of returns matters the moment you start withdrawing money, how to reverse the formula to solve for years or for an ending value, and how the same arithmetic applies to dividend growth and business metrics. Bring your own start and end figures to the retirement number calculator as you read, and see our interest formulas breakdown for the compounding machinery underneath.

What CAGR actually measures

CAGR answers one question: if this investment had grown by the same percentage every single year, what percentage would that have been? It takes a messy record of ups and downs and replaces it with the smooth path that would have arrived at exactly the same finish line. Nothing about that smooth path is claimed to be true. It is a construction, deliberately chosen because it is the one growth rate consistent with both endpoints and the elapsed time.

That construction is why CAGR is so useful for comparison. A result of 42 percent over four years and a result of 31 percent over three years are impossible to rank by eye, because the periods differ. Convert both to an annual compounding speed and they line up on the same scale immediately. Every serious performance table you meet reports annualized figures for this reason, and CAGR is the simplest member of that family.

It is worth being precise about the inputs, because they are the whole calculation. CAGR needs a beginning value, an ending value, and the number of years between them. It does not need the yearly returns, the volatility, the deposits, or the withdrawals. That thinness is both the strength and the weakness, and most misuse traces back to forgetting the second half of that sentence.

The CAGR formula written out in plain words

Start by dividing the ending value by the beginning value. That gives you the growth multiple: 1.5 means you finished with half again as much as you started, 2 means you doubled, 0.75 means you kept three quarters of what you had. This single number captures the whole result of the period, but it says nothing about how long the period was, which is the piece CAGR adds next.

Now take the nth root of that multiple, where n is the number of years. The nth root asks what number, multiplied by itself n times, produces the multiple. On a calculator this is the same as raising the multiple to the power of one divided by n. Finally, subtract one and multiply by 100 to state the answer as a percent. In one line: CAGR equals the ending value divided by the beginning value, raised to the power of one over the number of years, minus one.

Two mechanical notes matter more than they look. First, the exponent must be one divided by the years, not the years themselves, because you are undoing compounding rather than applying it. Second, n is the number of intervals, not the number of data points. Ten year-end values spanning a decade give you nine intervals, not ten, and that single off-by-one error is the most common way a correct formula returns a wrong answer.

A worked calculation from beginning value to answer

Take an illustrative stake of 10,000 dollars that is worth 20,000 dollars ten years later, with no money added or removed along the way. Step one: divide 20,000 by 10,000 to get a growth multiple of 2. Step two: raise 2 to the power of one tenth, which is the tenth root of 2, and comes to about 1.071773. Step three: subtract 1 to get 0.071773, then multiply by 100. The CAGR is about 7.18 percent a year.

Check it in reverse, which is always worth doing. Multiply 10,000 by 1.071773 ten times over and you land back on 20,000. The check works because the nth root and the nth power undo each other exactly, so a correct CAGR always rebuilds the ending value from the beginning value. If your reversal misses, the error is nearly always in the year count or in the exponent.

Try a less tidy set to prove the method is not relying on round numbers. An illustrative 10,000 dollars that grows to 17,500 dollars over seven years has a multiple of 1.75. The seventh root of 1.75 is about 1.083228, so the CAGR is roughly 8.32 percent. Nothing about the arithmetic changed; only the numbers did. Run your own beginning and ending values through the retirement number calculator to see how a modest change in the rate moves a long-horizon result.

Why CAGR is a geometric mean and not an average

An arithmetic average adds things up and divides by how many there are. That is the right tool when the items are independent, like the heights of a group of people. Investment returns are not independent in that sense, because each year’s return applies to whatever the previous year left behind. They chain together by multiplication, not addition, and a mean that adds them is answering a question nobody asked.

The geometric mean is the version built for chained quantities. Instead of summing the returns and dividing, it multiplies the growth factors together and takes the nth root of the product. That is precisely what the CAGR formula does, just with the multiplication already collapsed into the ratio of ending value to beginning value. So CAGR is not merely similar to a geometric mean; it is one, computed on the growth factors of the period.

This is not a technicality. The geometric mean is the only average that reproduces the actual ending balance when you apply it year after year. Apply the arithmetic average to a volatile series and you finish somewhere the money never went. The rest of this breakdown leans on that distinction, because almost every misleading growth claim you will encounter is an arithmetic average wearing an annual-return label.

The plus fifty then minus fifty demonstration

Here is the cleanest proof that the arithmetic average lies. An illustrative 10,000 dollars gains 50 percent in year one, taking it to 15,000 dollars. In year two it loses 50 percent, which is 7,500 dollars off a 15,000 dollar base, leaving 7,500 dollars. The arithmetic average of plus 50 and minus 50 is exactly zero, so an average-based summary would report a flat two years. The account is down 25 percent.

Run the CAGR properly on the same facts. The multiple is 7,500 divided by 10,000, which is 0.75. The square root of 0.75 is about 0.866025. Subtract one and the CAGR is roughly negative 13.40 percent a year. Applied twice, 10,000 times 0.866025 twice over returns 7,500 dollars, matching the balance exactly. The geometric answer reconciles; the arithmetic answer does not.

The asymmetry has an intuitive cause. The 50 percent gain was earned on 10,000 dollars and added 5,000. The 50 percent loss was taken on 15,000 dollars and removed 7,500. Equal percentages applied to unequal bases produce unequal dollars, and the larger base belongs to the loss whenever the gain came first. Reverse the order and the ending value is identical, because multiplication does not care about sequence.

Arithmetic average versus CAGR on a five year record

The two-year example is deliberately extreme. A more ordinary record shows the same effect at a realistic scale. Take an illustrative five year sequence of returns: plus 20 percent, plus 10 percent, minus 15 percent, plus 25 percent, and minus 5 percent. Add them and divide by five and you get an arithmetic average of exactly 7.00 percent a year, which is the figure most people would quote.

Now compound them. Multiplying 1.20, 1.10, 0.85, 1.25 and 0.95 together gives about 1.332375, so an illustrative 10,000 dollar stake finishes at roughly 13,324 dollars, a total return of about 33.24 percent. The fifth root of 1.332375 is about 1.059072, making the CAGR roughly 5.91 percent. The two summaries of the same five years differ by 1.09 percentage points, and only the lower one produces the ending balance that is actually in the account.

That gap is called volatility drag, and it is not a rounding artifact. It scales with how spread out the returns are: a calm series with returns clustered near the mean shows almost no gap, while a wild series shows a large one. Two records with the same arithmetic average can therefore deliver very different money, and the CAGR is what tells them apart. Our dividend stock evaluation note makes a related point about smooth-looking averages hiding uneven underlying results.

What CAGR deliberately hides

CAGR is built from two data points. Everything between them is discarded by construction, which means the measure is silent on the things that decide whether an investor could actually hold on. It cannot tell you the worst drop along the way, how long the position spent below its previous high, or whether the gains arrived in one lucky stretch or accumulated steadily. All of that vanishes into the smoothing.

That silence is not a flaw in the formula, but it becomes a flaw in the reader who forgets it. A 7.18 percent CAGR sounds like a savings account with a good rate. It could equally describe a holding that halved at some point and clawed back everything and more. Same number, entirely different experience, and entirely different odds that a real person stayed invested through it.

The practical habit is to treat CAGR as one column in a table rather than the whole table. Alongside it, ask for the largest peak-to-trough decline over the period, the number of negative years, and the shape of the recovery. None of those require advanced math, and together they turn a single smooth figure into an honest description. Our 4 percent rule analysis walks through why the shape of a return series, not just its average, drives whether a plan survives.

Two investments one CAGR two very different rides

Picture two illustrative holdings that both start at 10,000 dollars and both finish at 20,000 dollars after ten years. By definition they share a CAGR of about 7.18 percent, and any performance table that reports only annualized growth will show them as equals. That equality is real in one narrow sense and misleading in every other.

The first holding rose in small steps most years, dipped modestly twice, and never fell more than a fraction below its previous peak. Holding it required patience and nothing else. The second fell by close to half in its second year, spent several years recovering, then rose sharply near the end to reach the same finish line. Holding that one required conviction through a period where the account showed a large loss, and many owners would have sold.

Both stories end at 20,000 dollars, so both produce the same CAGR. The difference matters most for anyone who might need the money at an unplanned moment, or who might not have the temperament for the second path. This is why the sensible reading of CAGR is comparative rather than descriptive: use it to rank results on a common scale, then look at the underlying series before treating two equal numbers as equivalent choices.

Sequence of returns and why it matters when you withdraw

Because multiplication is order-independent, a lump sum left alone finishes in the same place no matter how the yearly returns are shuffled. Take the five returns above and reverse them entirely, and the ending value is still about 13,324 dollars and the CAGR is still about 5.91 percent. Many people stop there and conclude that order never matters. It stops being true the moment money moves in or out.

Add withdrawals and the arithmetic changes. Start with an illustrative 100,000 dollars and take out 6,000 dollars at the end of each year while the same five returns play out. In the order given, with the strong years first, the balance finishes near 101,694 dollars. Run the identical returns in reverse, so the weak years come first, and the balance finishes near 96,971 dollars. Same returns, same CAGR, a difference of roughly 4,723 dollars over five years.

The cause is that a withdrawal taken during a down year sells a larger share of the portfolio, and those units are never there to recover. Over a multi-decade retirement the same mechanism compounds into outcomes that diverge dramatically. A CAGR, which is blind to ordering, cannot warn you about any of it, which is why withdrawal planning is done with sequences rather than with a single average rate.

CAGR versus total return

Total return and CAGR describe the same result from two angles. Total return is the whole percentage change: ending value divided by beginning value, minus one. In the doubling example it is 100 percent. CAGR takes that same change and asks how fast it happened, which requires knowing the elapsed time. Neither figure is more correct; they answer different questions and are misread mainly when one is quoted as if it were the other.

The distinction bites hardest with long periods. A 100 percent total return over three years is a CAGR near 26 percent, which would be a remarkable result. The identical 100 percent total return over thirty years is a CAGR near 2.3 percent, which would trail a decent savings account. The headline number is unchanged; only the clock differs, and the clock is what decides whether the result was excellent or poor.

There is also a shortcut that seems reasonable and is not: dividing the total return by the number of years. On the doubling example, 100 percent divided by ten gives 10 percent a year, against a true CAGR of 7.18 percent, an overstatement of 2.82 percentage points. That shortcut ignores compounding entirely, and it always flatters the result. If a growth figure looks suspiciously round, this is often how it was produced.

How CAGR relates to annualized and money weighted returns

CAGR sits inside a family of annualized return measures, and knowing the neighbors prevents mismatched comparisons. The broadest term is simply annualized return, meaning any result restated as a per-year compounding rate. CAGR is the plainest member: two endpoints, one elapsed time, no cash flows considered.

Time-weighted return chains together the return of each sub-period, so that deposits and withdrawals do not distort the picture. It is the standard for judging how an investment or a manager performed, because it isolates the performance from the timing of the money. When there are no cash flows at all, the time-weighted return and the CAGR of the same period agree.

Money-weighted return, often computed as an internal rate of return, does the opposite: it accounts for how much money was present at each moment, so contributing heavily right before a strong stretch raises it. That makes it the better measure of what an individual investor personally earned. The rule of thumb is to compare an investment using time-weighted or CAGR figures, and to measure your own experience with a money-weighted figure. Comparing one against the other is a common source of arguments about numbers that were never measuring the same thing.

Comparing investments measured over different periods

The moment two results cover different spans, raw percentages become uncomparable, and this is where CAGR earns its keep. A holding up 42 percent over four years has a multiple of 1.42 and a CAGR near 9.15 percent. Another up 31 percent over three years has a multiple of 1.31 and a CAGR near 9.42 percent. The smaller headline is the faster grower, which no amount of staring at 42 versus 31 would have revealed.

Converting to a common annual rate is the entire point of the exercise, and it works across asset types too. A rental property, a savings balance, a business line and a share holding can all be reduced to a growth rate per year and lined up side by side. Whether they should be compared is a separate question involving risk, liquidity and taxes, but the arithmetic obstacle disappears.

Keep two disciplines when comparing. Use the same span for every candidate where possible, because different windows include different market conditions. And compare like with like on what is counted: a price-only growth rate ignores income, so it will understate a holding that paid cash along the way. Our note on how dividend yield works explains why leaving income out of a growth figure can change the ranking completely.

The cherry picked start and end date trap

CAGR depends entirely on two points, which makes it trivially easy to manipulate by choosing them. Move the start date to a low point and the growth rate leaps. Move the end date to a peak and it leaps again. Nothing dishonest has to be stated; the presenter simply selects the window, and the arithmetic does the rest, faithfully and correctly.

Consider an illustrative series that starts at 100 and runs through ten years of ups and downs, finishing at 196. Over the full ten years the CAGR is about 6.96 percent. Start counting from the low point at the end of year two, when the series sat at 84, and the remaining eight years produce a CAGR of about 11.17 percent. Pick the flat stretch from year one to year six, from 118 to 128, and the same investment shows about 1.64 percent. Same data, three defensible-sounding numbers.

The defense is procedural rather than mathematical. Ask what the start and end dates are before you accept any growth rate, prefer full periods over windows that begin at a trough, and check whether the same rate holds over a longer span. A figure that collapses when you extend the window by a year was measuring the window, not the investment.

Where a compounded ending value comes from

It helps to see where a compounded result actually accumulates, because the shape explains why late years dominate. Using the same illustrative series that runs from 100 to 196 over ten years, the starting value accounts for a little over half of the finish. The first five years add 32 points of growth, taking the series from 100 to 132. The final five years add 64 points, twice as much, taking it from 132 to 196.

The lopsided split is compounding made visible. The second half of the period did not enjoy better luck; it simply worked on a bigger base, so identical percentage moves produced bigger point moves. This is the same effect that makes the tail end of a long savings horizon add more dollars than the early years despite identical contributions, which our S&P 500 contribution analysis traces through decades of monthly investing.

It also explains why cutting a horizon short is so costly. Losing the last three years of a compounding period removes the largest dollar gains, not the smallest, because those years were operating on the highest base. A CAGR calculated on a truncated window will look reasonable while the money forgone is disproportionate to the years given up.

Using CAGR for dividend growth rates

CAGR is not only a price measure. One of its most practical uses is measuring how fast a cash payment has grown, because the same three inputs apply: a beginning payout, an ending payout, and the years between. An illustrative dividend of 1.20 dollars per share that reaches 2.10 dollars per share eight years later has a multiple of 1.75, and the eighth root of 1.75 is about 1.072457, giving a dividend growth rate near 7.25 percent a year.

That single figure is more informative than a list of yearly raises, because raises are lumpy. A payer might hold flat for two years and then jump, or split a large increase across several small ones. Compressing the record into one annual rate lets you compare a steady raiser against a lumpy one on the same scale, and lets you compare across payers whose records cover different lengths of time.

The cautions carry over exactly. A dividend growth rate measured from a year in which the payout was unusually depressed will overstate the trend, and one measured to a year with a special or one-time payment will overstate it further. Check whether the endpoints are ordinary, and read the growth rate alongside the payout ratio rather than on its own; our dividend evaluation note covers the sustainability side of that question.

Using CAGR for revenue earnings and other business metrics

The same formula travels well beyond investing. Revenue, unit sales, subscribers, headcount, rent, tuition and household spending all have a beginning value, an ending value and an elapsed time, and all can be summarized as a compound annual growth rate. An illustrative business growing revenue from 40 million dollars to 95 million dollars over six years has a multiple of 2.375, whose sixth root is about 1.155076, giving a CAGR near 15.51 percent.

This is why growth rates in company filings and market reports are usually annualized. It lets a five year revenue record be compared against a three year one, or a fast-growing small line against a slow-growing large one. It also lets you separate the growth rate from the base, which matters because a large percentage on a small base and a small percentage on a large base can add identical dollars.

Two extra cautions apply to business figures. Metrics that can be negative, such as earnings, break the formula outright when the beginning value is at or below zero, since the ratio becomes meaningless. And metrics that were restated, reclassified or affected by an acquisition are not measuring the same thing at both ends, which makes the growth rate a comparison between two different definitions rather than a measure of growth.

Reversing the formula to find the years you need

The CAGR equation has four quantities: beginning value, ending value, years, and rate. Know any three and you can solve for the fourth, which makes it a planning tool rather than only a reporting one. Solving for years requires logarithms, but only one line of them.

The number of years equals the natural log of the ending value divided by the beginning value, all divided by the natural log of one plus the rate. As an illustration, growing 10,000 dollars to 25,000 dollars at an assumed 8 percent takes the log of 2.5, which is about 0.9163, divided by the log of 1.08, which is about 0.0770. The answer is roughly 11.9 years. Any log button on a calculator or spreadsheet will do it, and the base does not matter as long as both logs use the same one.

The honest caveat is that this reversal is only as good as the rate you assume, and assumed rates are not promises. Investment returns are uncertain in both direction and timing, so treat the answer as a rough planning horizon rather than a date. It is still useful, because it converts a vague goal into a testable statement: at this assumed rate, this target is about twelve years away, and if the rate disappoints, it is further.

Reversing the formula to find an ending value

Solving for an ending value is the easier direction, because it needs no logs. Multiply the beginning value by one plus the rate, raised to the power of the number of years. An illustrative 10,000 dollars compounding at 7.18 percent for ten years returns 20,000 dollars, which is the same example running forward instead of backward. Extend it to 25 years at the same rate and it reaches roughly 56,569 dollars.

That extension is worth pausing on. Ten years produced 10,000 dollars of growth, while the following fifteen years produced roughly 36,569 dollars more, on an unchanged rate and with nothing added. The exponent, not the rate, is doing the work, which is the single most useful thing the reversed formula teaches. Our interest formulas breakdown walks through the same asymmetry in more detail.

Use the reversal in both directions when you plan. Forward, it tells you where a rate and a horizon land. Backward, it tells you what rate a target would require, which is often the more sobering answer. If a goal demands a rate far above what a diversified portfolio has historically produced, the honest fix is usually a longer horizon or a larger contribution rather than a riskier assumption. The retirement number calculator is a quick way to see how those three levers trade off against each other.

The rule of 72 as a sanity check on CAGR

The rule of 72 is a mental shortcut for doubling time: divide 72 by the annual growth rate and you get roughly the number of years for a balance to double. It is not exact and it is not derived from the CAGR formula, but it approximates the answer closely enough over the range of rates most investors deal with, and it makes an excellent error check.

On the running example, a 7.18 percent CAGR gives 72 divided by 7.18, which is about 10.03 years to double. The example doubled in exactly ten years, so the shortcut lands almost on top of the true answer. That agreement is a signal that the CAGR was computed correctly. When a quoted growth rate and a known doubling time disagree badly, something is wrong with one of them, and it is usually the year count.

Run the check whenever a growth claim arrives without workings. If a page says an investment grew at 15 percent a year for a decade, the rule implies roughly a doubling every five years, so about a fourfold increase over ten. If the stated ending value is nowhere near four times the start, the rate and the values do not describe the same investment. The shortcut costs five seconds and catches a surprising share of bad numbers.

Common mistakes that produce a wrong CAGR

The most frequent error is counting years wrong. Values recorded at the end of each year from 2015 to 2025 look like eleven numbers, and they are, but they span ten intervals. Using eleven as n understates the growth rate; using nine overstates it. Count the gaps between the endpoints, not the observations.

The second is dividing the total return by the number of years, which ignores compounding and always produces a friendlier figure. The third is applying the formula to a beginning value of zero or a negative number, which makes the ratio undefined or nonsensical; no valid growth rate exists in those cases, and the honest reporting is to say so rather than to substitute a placeholder.

Two more are subtler. Mixing periods, such as computing a rate on quarterly data and then labeling it annual, silently misstates the answer by a factor buried in the exponent; keep n in the same unit as the rate you intend to report. And ignoring cash flows turns CAGR into nonsense: if money was added or withdrawn during the period, the ending value reflects those transfers as well as growth, and the rate you calculate will credit deposits as performance. Fractional periods are fine, incidentally: three and a half years is simply an n of 3.5.

When CAGR is the wrong tool

Skip CAGR when money moved in or out during the period. A portfolio that received regular contributions will show an inflated growth rate, because the formula treats every extra dollar of ending value as growth regardless of where it came from. For contribution-heavy accounts, a money-weighted return or a proper contribution-adjusted calculation is the right measure, and our dollar cost averaging analysis shows how steady deposits reshape an ending balance.

Skip it over very short periods too. Annualizing a three month result multiplies whatever happened in those months by roughly four in compounding terms, which turns ordinary noise into an implausible annual rate. A quarter that gained 12 percent annualizes to something near 57 percent, a number nobody should repeat as if it described a year.

Be careful with any series that crosses zero or changes definition, and with comparisons where one figure includes income and the other does not. Finally, be careful in high-inflation stretches, where a nominal growth rate can look healthy while purchasing power fell. If the question is about real gains, deflate both endpoints first and calculate the rate on those, and label clearly whether the figure you are quoting is nominal or real.

Reading a CAGR someone else calculated

When a growth rate arrives from somewhere else, four questions settle whether it means anything. What were the exact start and end dates? What were the two values? Does the figure include income such as dividends or interest, or price only? And were there any deposits, withdrawals or other cash flows in between?

If those four answers are available, the rate is checkable, and checking takes under a minute with the formula above. If they are missing, the rate is a claim rather than a measurement, and it deserves the skepticism you would give any unsourced number. Presenters who are confident in their figures state the window; presenters who are not tend to leave it out.

Two extra flags are worth watching. A start date that sits at an obvious low point in the series suggests the window was chosen rather than found. And a rate quoted to two decimal places on data that only supports one is a presentation of precision that the inputs cannot deliver. Neither is proof of anything dishonest, but both are reasons to ask for the full series before treating a growth rate as settled.

How to use CAGR without fooling yourself

Adopt a short routine and CAGR becomes reliable rather than persuasive. Always state the window with the rate, so that any figure you produce travels with the information needed to verify it. Always count intervals rather than data points. Always check the result by compounding it forward and confirming it lands on the ending value you started from.

Then read it in context. Put the largest decline over the period next to the growth rate, note how many years were negative, and consider whether the same rate survives a longer window. If it does not, you are looking at a favorable stretch rather than a durable trend. Where cash flows exist, switch measures rather than forcing the formula, and where inflation matters, say whether the figure is nominal or real.

Above all, remember what the number is: a construction that reproduces a finish line, not a description of the journey. Used that way it is one of the most useful arithmetic tools an ordinary investor can carry. Used as a promise about the future, it is just a smooth curve drawn through two points, and the market has no obligation to follow it. Test your own start and end figures in the retirement number calculator rather than accepting anyone’s headline rate.

The bottom line

CAGR converts any result over any length of time into a single comparable speed: divide the ending value by the beginning value, take the nth root, subtract one. It is a geometric mean, which is why it always sits at or below the arithmetic average of the same yearly returns, and why a plus 50 then minus 50 pair that averages zero actually leaves an illustrative stake down 25 percent, a CAGR near negative 13.40 percent. The compounded number is the one that matches the money.

What CAGR cannot do is describe the ride. It ignores volatility, the depth of drawdowns, the order of returns, and every dollar that moved in or out along the way, and it can be steered almost anywhere by the choice of start and end dates. Use it to line up results on a common scale, verify it by compounding forward, reverse it to test how long a goal would take, and then look past it before concluding that two identical rates describe two comparable investments. Every figure in this article is illustrative, and the arithmetic is the only part of it you should treat as settled.

Dividora publishes independent educational analysis, and nothing above is personalized investment, tax, or financial advice. All values, growth rates, series and worked examples here are invented illustrations chosen to make the arithmetic clear, not observations of any real market, security, or company, and no rate shown should be read as a forecast of what any investment will do. Compound growth rates describe the past only, actual returns arrive unevenly and can be negative for long stretches, and any projection built on an assumed rate will be wrong to some degree. Before acting on a growth figure of your own, confirm the underlying values and dates yourself and discuss the decision with a qualified financial professional who can weigh your full circumstances.

Edited by Hamza Hai, MBA · Editor

Hamza Hai is the editor of Dividora. She holds an MBA and reviews the site's articles against our editorial standards, checking that every figure is labelled for what it is, that nothing is presented as verified fact without a source the reader can check, and that the writing stays useful to a non-specialist.

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