A coworker asked me a question at lunch last month that I could not answer on the spot.
He had just opened his first investment account. He wanted to know one thing: “If I leave this alone, how long until it doubles?”
I have been buying an index fund every month for years. I have written on this site about dollar-cost averaging, about what an ETF actually is, about why I do not pick stocks. And I could not answer a one-sentence question about my own money without opening a spreadsheet.
That bothered me enough to go learn the answer properly. It turns out there is a piece of arithmetic from 1494 that does it in your head, in about three seconds. It is called the Rule of 72, and it is the only compound interest math I actually use.
This post is the explanation I wish someone had given me before I started.
First, the thing compound interest actually is
Most explanations start with a definition. Definitions did not help me. What helped me was seeing the fork.
Imagine you put in 1,000 dollars and it earns 7 percent a year.
Simple interest pays you 70 dollars every year, forever. Year one, 70 dollars. Year thirty, 70 dollars. After thirty years you have 1,000 dollars of principal plus 2,100 dollars of interest. Total: 3,100 dollars.
Compound interest pays you 70 dollars in year one, and then next year it pays 7 percent on 1,070 dollars instead of 1,000. So year two pays 74.90. Year three pays 80.14. The payment itself grows, because the thing being paid on grows.
After thirty years, that same 1,000 dollars is 7,612 dollars.
Same money in. Same rate. Same number of years. The difference is 4,512 dollars, and all of it comes from one detail: whether the interest gets to earn interest.
That is the entire idea. Everything else is bookkeeping.
The part that took me longer to accept is that the gap between those two lines is not steady. It is small for a long time and then it is enormous. Which brings me to the shortcut.
The Rule of 72
Here is the whole rule:
Divide 72 by your annual return. The answer is roughly how many years until your money doubles.
That is it. No calculator.
- At 6 percent: 72 divided by 6 equals 12 years to double.
- At 7 percent: 72 divided by 7 equals about 10.3 years.
- At 9 percent: 72 divided by 9 equals 8 years.
- At 2 percent, closer to what a savings account pays: 72 divided by 2 equals 36 years.
That last one is the number that actually changed my behavior. Money sitting in a low-interest account is not standing still. It is doubling — on a timeline longer than most working careers.
The rule is old. It appears in Summa de Arithmetica, published in Venice in 1494 by Luca Pacioli, the friar usually credited with documenting double-entry bookkeeping. He wrote it down as common knowledge among merchants, not as a discovery. People have been doing this arithmetic on their fingers for over five hundred years.
Why 72, and where the rule breaks
I do not like using a formula I cannot check. So I checked it.
The exact answer comes from logarithms: true doubling time is ln(2) divided by ln(1 + r). The number 72 is a convenient stand-in because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12.
Here is how far off it actually is:
| Annual return | True doubling | Rule of 72 | Error |
|---|---|---|---|
| 2 percent | 35.00 years | 36.00 years | 1.00 year |
| 4 percent | 17.67 years | 18.00 years | 0.33 year |
| 6 percent | 11.90 years | 12.00 years | 0.10 year |
| 7 percent | 10.24 years | 10.29 years | 0.04 year |
| 8 percent | 9.01 years | 9.00 years | 0.01 year |
| 12 percent | 6.12 years | 6.00 years | 0.12 year |
| 20 percent | 3.80 years | 3.60 years | 0.20 year |
Look at the middle of that table. Between 6 and 9 percent, the rule is accurate to within about a month.
That is a useful accident. The S&P 500 has returned roughly 10.4 percent a year nominally since 1957, or about 6.8 percent after inflation. The band where the Rule of 72 is nearly exact is the band a long-term index investor actually lives in.
It gets sloppy at the extremes. At 20 percent it is off by more than two months per doubling, and errors compound. But if someone is quoting you 20 percent, the arithmetic error is not your biggest problem.
The part nobody puts on the poster
Here is where I had the idea wrong for years.
I thought of compounding as a smooth hill. It is not. It is almost flat, and then it is a wall.
Take 500 dollars a month at 7 percent for forty years. Here is what each decade contributes:
| Decade | Grows from | Grows to | Added |
|---|---|---|---|
| Years 1-10 | 0 | 86,542 | 86,542 |
| Years 11-20 | 86,542 | 260,463 | 173,921 |
| Years 21-30 | 260,463 | 609,985 | 349,522 |
| Years 31-40 | 609,985 | 1,312,407 | 702,421 |
The final balance is 1,312,407 dollars. You put in 240,000 dollars. Eighty-two percent of that account is growth, not deposits.
And look at the last row. The final decade alone added 702,421 dollars — fifty-four percent of the entire outcome arrived in the last ten years.
More than half the result shows up in the last quarter of the time.
This explains something I never understood about people who quit investing. If you start, do it faithfully for eight years, and then look at your balance, you have not seen compounding yet. You have mostly seen your own deposits with a modest tip on top. It feels like it is not working, because at that point it genuinely does not look like it is working.
The reward for the first decade is not the money. It is the second decade.
So what if you start in your 40s?
I am a 40-something engineer. I did not start with a plan in my twenties. I want to be honest about what that costs, because most articles on this topic are not.
Same 500 dollars a month, same 7 percent:
| Starting point | Years invested | Ending balance |
|---|---|---|
| Start at 25 | 40 years | 1,312,407 |
| Start at 35 | 30 years | 609,985 |
| Start in your 40s | 22 years | 312,323 |
Starting eighteen years later does not cost you 45 percent of the result. It costs you 76 percent of it. The years you skip are the expensive ones, because they are the ones that would have been at the far right of the curve doing the heavy lifting.
That is the real answer to “is it too late,” and it is not a comfortable one. Late starters cannot buy back the tail. Anyone who tells you otherwise is selling something.
But there is a second half to this, and it is the reason I keep going.
The tail is measured from today, not from your birthday. I publish my savings figure on this site — as of my last monthly recap it was 106,514 dollars. Run the Rule of 72 on it and something obvious falls out: at 7 percent, that number doubles in about 10.2 years whether or not I ever deposit another dollar.
Left completely alone for two more decades, it becomes roughly 401,000 dollars. That is not a projection I invented; it is 106,514 multiplied by 1.07 nineteen times, and you can check it on your phone.
The money already in the account does not know how old I am. It only knows how long it gets left alone.
The three things that quietly break it
If compounding is mostly the last stretch, then anything that shortens the stretch or shaves the rate is far more expensive than it looks. Three things do this.
1. Fees
This is the one that shocked me. Same 500 dollars a month, same forty years, same 7 percent gross return — only the annual expense ratio changes:
| Annual fee | Ending balance | Cost of the fee |
|---|---|---|
| 0.00 percent | 1,312,407 | — |
| 0.30 percent | 1,206,876 | 105,531 |
| 1.00 percent | 995,745 | 316,662 |
| 1.50 percent | 870,520 | 441,887 |
A 1 percent annual fee does not cost you 1 percent. Over forty years it costs you 24 percent of the final account. The fee is charged on the balance, which means it is charged hardest exactly when the balance is largest — during the years that were supposed to be your payoff.
This is the entire practical argument for low-cost index funds, and it is arithmetic, not ideology.
2. Taxes paid along the way
Every dollar paid in tax before the finish line is a dollar that stops compounding. This is why tax-sheltered retirement accounts are so powerful, and I wrote about that separately in the secret weapon behind America’s 401(k) millionaires.
3. Selling
Selling resets the clock on the portion you sold. Not the rate — the clock. You go back to the flat part of the curve with that money. This is the least visible of the three because it never appears on a statement as a cost.
Korea does not hand you this. You have to build it.
There is a structural point I cannot skip, because it is the difference between the American articles you will read on this subject and the situation I am actually in.
In the United States, an ordinary employee gets a 401(k): payroll deduction, employer match, decades of tax-deferred compounding, all running by default. Fidelity counted 645,000 401(k) millionaires at the end of the first quarter of 2026. Almost none of them picked winning stocks. They were enrolled in something that quietly compounded for thirty years while they did their jobs.
Korea has no equivalent default. What we have instead are accounts you must open and fund yourself: a personal pension account (연금저축) and an individual retirement pension (IRP), which together carry a combined annual tax-deduction ceiling of 9 million won. Below a certain income threshold the credit rate is 16.5 percent, and above it, 13.2 percent.
The tax break is real and worth using. But nobody enrolls you. Nobody matches you. No default exists to carry you while you are not paying attention.
So the compounding engine that runs automatically for an American office worker is, here, a machine you have to assemble and switch on yourself. I wrote more about that gap in why a Costco cashier’s 401(k) story is harder to repeat in Korea.
That is not a complaint. It is the job description.
Where this goes wrong
I would not trust this post if it did not include this section.
Seven percent is an average, not a schedule. The market does not deliver 7 percent annually. It delivers 22 percent, then negative 18, then 9. The Rule of 72 assumes a constant rate, which never happens. It tells you the shape of the outcome, not the path.
The order of returns matters enormously. A bad decade at the end, when the balance is large, does far more damage than a bad decade at the start. Every table above quietly assumes the sequence cooperates. Mine may not.
645,000 millionaires is the tail, not the norm. The same Fidelity data reports an average 401(k) balance of about 141,000 dollars, and the millionaire count actually fell about 3 percent from the previous quarter as markets wobbled. The headline number is survivorship. The average is the reality.
Inflation is not in these numbers. Every figure above is nominal. The inflation-adjusted long-run return is closer to 6.8 percent, and 1.3 million dollars in forty years does not buy what 1.3 million dollars buys today. Compounding grows the number faster than inflation erodes it — but not by as much as the number suggests.
And I could simply be wrong about my own discipline. The math assumes I keep depositing through a 40 percent drawdown. I have never been tested by one.
FAQ
How long does it take to double my money at 7 percent?
About 10.3 years by the Rule of 72; 10.24 years exactly. At 6 percent it is 12 years, at 10 percent about 7.2 years.
Does the Rule of 72 work for debt?
Yes, and it is more urgent there. A credit card at 18 percent doubles the balance in about four years. Compounding is indifferent to which side of the ledger you are on.
Should I use 72 or a real calculator?
Use 72 for judgment in the moment — comparing two options, sanity-checking a claim. Use a real calculation for decisions that involve actual money.
Is it too late to start in my 40s?
No, but it is more expensive, and pretending otherwise does not help. See the table above: eighteen years of delay costs about three-quarters of the outcome. What is still available to you is the doubling of every dollar you put in from today, and the doubling of everything already sitting there.
What return should I assume?
I use 7 percent for planning because it is roughly the long-run inflation-adjusted return of a broad US index. I do not treat it as a promise.
What I actually took away
I did not learn a new investment strategy writing this. I kept buying the same index fund on the same day of the month.
What changed is that I stopped thinking of the boring middle years as a waiting room. Years 11 through 20 are not the dull part before the good part. They are the part that builds the balance that the good part gets to work on.
And I can finally answer my coworker’s question at the lunch table, in about three seconds, without a spreadsheet.
I am an engineer writing about my own money, not a financial advisor. Nothing here is investment advice. The arithmetic in this post is arithmetic — you can and should check it yourself — but what to do with it depends on your own situation, and that is your call, not mine.