The Magic of Compounding

This is part of Start Now — a complete guide to building your own tax-free pension, published free, one piece at a time. New here? Start Here →Years ago I tried to explain compounding to our eldest son at the kitchen table, and I could see it wasn’t landing. So we built a spreadsheet.The first one showed his money growing the way a bank grows it: the same small amount added each year, a straight line marching politely across the page. Fine. Boring. Understandable.Then we built a second one, where the growth was allowed to earn growth of its own. For the first ten years the two lines sat nearly on top of each other, and he was unimpressed. Around year fifteen they began to separate. By year thirty the first line was still marching along the bottom of the screen and the second had walked off the top of it.That is this chapter in a single image, and it is the part almost nobody feels until they see it: compounding is boring for a long time, and then it isn’t. The dullness of those early years is not a sign that it isn’t working. It is exactly what it looks like when it is working. For ten years they look like the same decision. They aren't.Compounding is the simple idea that the returns you earn begin to earn returns of their own. A dollar of gain, left invested, becomes a base for the next year’s gain, and the year after that, and the year after that, etc. Over a few years the effect is almost invisible. Over a working lifetime it becomes the single most powerful force in personal finance. This first section builds the intuition for why that is, why the effect becomes dramatic only after a couple of decades, and why, despite the stock market’s year-to-year turbulence, long holding periods have historically been remarkably dependable.Here is that engine in its simplest form: what a single dollar invested at age 30 becomes by various ages, at the 10% long-run return:Growth of $1 at a 10% annual return. The same multiplier applies to any contribution.A person who invests $1,000 in a single year at age 30 has roughly $45,000 from that one year’s contribution by age 70, when it grows at the 10% long-run compound return of the stock market as measured by the S&P 500; someone who does it every year accumulates the millions shown in the case studies. The multiplier is the lesson, not the size of the contribution.1.1Linear growth versus exponential growthIt helps to start with the contrast between simple interest and compound interest – or linear growth versus compound growth. With simple interest, you earn the same fixed amount every year, because the gains are skimmed off rather than reinvested. Growth is a straight line. With compound interest, the gains stay in the account, and those gains go on to earn gains of their own. Growth earns growth. The line stops being straight and starts to curve upward, gently at first and then steeply.Consider a single $10,000 investment earning 7% a year. This 7% is the stock market’s long-run return after subtracting inflation, its “real” return, which is simply the 10% nominal return used elsewhere in this book , less long-run inflation. Simple interest on it adds a flat $700 every year, forever. Compounding adds 7% of an ever-larger balance: $700 in year one, $749 in year two, $1,287 in year ten, and nearly $9,800 in year forty. The table below shows how the two diverge.A single $10,000 investment at 7%. The advantage of compounding is trivial early but overwhelming later on.1.2The rate of return matters enormously, eventuallyNot all compounding is equal. When you invest in a bank CD or money-market fund, where your money gets reinvested daily, the returns compound too, but at a relatively low rate, call it 4%. A diversified stock portfolio has historically compounded at roughly 10% including reinvested dividends, its long-run compound return since 1928 (more on that figure shortly, and in full in Deep Dive A, “The Return Assumptions”). In the early years these two paths look almost the same, which is exactly why the difference is so easy to underestimate. Given enough time, though, the higher rate doesn’t just win. By year forty the stock path is worth roughly nine times the CD path.A single $10,000 investment.1.3Why it “goes vertical” after 20–30 yearsThe curve’s late steepness is not an illusion or a quirk of the chart. It is the mathematics of repeated doubling.A useful shortcut, the “Rule of 72,” says money doubles in roughly 72 divided by the return rate. At 10%, that is about every 7.2 years. At 4 percent, the kind of return cash or safe bonds might earn, the same money takes about 18 years to double, about two and a half times as long.The crucial point is that every doubling is larger in absolute dollars than all the growth that came before it combined. Going from $1 million to $2 million adds a full million dollars in a single step, as much as the entire climb from $10,000 up to $1 million put together. Because the early doublings happen on small balances, the first two decades feel slow; because the late doublings happen on large balances, the final two decades feel almost unreal. This is why starting early is worth so much more than saving more later: the early dollars are the ones that get to double the greatest number of times.Run your own numbersEvery figure in this book comes from the same three inputs: what you put in, how long it compounds, and at what rate. Change any one of them and the answer changes, which is why the case studies ahead are illustrations rather than targets.If you want to see your own version, the U.S. Securities and Exchange Commission publishes a free compound interest calculator at investor.gov. It takes about thirty seconds: enter what you have now, what you plan to add each month, the number of years, and a rate. Use 8 percent to see this book’s floor, 10 percent to see its average.It is a government education tool, so there are no ads, no sign-up, and nothing for sale. Just the arithmetic.1.4Stocks are volatile, but time tames the volatilityEverything in this book leans on the market's long-run average of about 10 percent a year, and here is the uncomfortable truth about that number: almost no single year looks anything like it. An average of 10 percent sounds calm, even boring. The reality it summarizes is anything but. In any single year the market might soar 50 percent or fall 40 percent, and a year that actually returns 10 percent is a rarity. So before trusting the average, look at the raw material it came from: every single year on its own.Chaos, year to year. And yet it matters far less over long horizons than most people expect, because good and bad years tend to offset one another, and the longer the holding period, the more reliably they do so. Take those same 98 years and hold them in combinations, every possible stretch of five, ten, twenty, thirty years, and watch the chaos compress. The chart below uses S&P 500 total returns (with dividends reinvested) for every year from 1928 through 2025. We compute the annualized return an investor would have earned over every possible holding period of a given length: every one-year stretch, every five-year stretch, and so on. The pattern is striking.Three results stand out:* 1. The average return is similar across every horizon, from +10.4% to +11.8%.* 2. No 20- or 30-year period was ever negative.* 3. Even the worst 30-year stretch in nearly a century still compounded at 8% a year; the best reached 13.6%1.Single-year returns can land anywhere from −44% to +53%, but stretch the horizon to thirty years and that spread collapses into a tight, entirely positive band of +8% to +13.6%. This is the empirical foundation for the conclusions and case studies that follow: over a multi-decade horizon, a broad stock index has behaved less like a gamble and more like a slow, dependable compounding machine.The base case used in this bookBecause the case studies span a full saving lifetime (roughly 30–40 years), the natural return assumption comes from the historical 30-year record, which runs from a worst case of 8.0% to a best case of 13.6%. As its base case, this book uses a long-run average of about 10%, the S&P 500’s compound return over the past century. Every conclusion in this book is built on the 8% floor; the tables show the 10% average alongside it, and Section 3.2 brackets every result with the 8% and 13.6% cases. A 10% assumption should be read as illustrative, not a forecast. Deep Dive A shows the full record behind this figure: every rolling 30-year return since 1928, and how it has moved over time.1.5Why a 4% withdrawal rate?Throughout the case studies, retirement income is illustrated as a 4% withdrawal. In plain terms: in your first year of retirement you take out 4% of your portfolio (for example, $40,000 from a $1 million balance). That figure is not arbitrary: it comes from one of the best-known ideas in retirement research, the so-called “4% rule.” In a 1994 study, financial planner William Bengen examined every 30-year retirement window in U.S. history and asked, “How much could a retiree take out in the first year, then increase by inflation each year, without running out of money?” His answer was about 4%, confirmed a few years later by three professors at Trinity University in a 1998 study that took the school's name. On a balanced stock-and-bond portfolio, an initial 4% withdrawal survived more than 95% of historical 30-year periods, including the worst case on record (a retiree who began in the late 1960s, just before a long stretch of high inflation)2.Crucially, 4% is a worst-case-derived number, and may even be a conservative one. Bengen himself noted that the average successful withdrawal rate across history was above 6%, and in favorable periods retirees could have safely taken even more. In his 2025 book, Bengen — the rule’s own creator — goes further, arguing that most retirees today can safely take closer to 5% to 5.5% (his updated worst-case, “never-failed” figure is about 4.7%). More cautious voices point the other way: Morningstar, weighing today’s valuations and bond yields, puts its 2026 base case at roughly 3.9%, and Vanguard suggests a 3.5–4% range3. This book deliberately uses the lower, classic 4% anyway — widely understood and genuinely cautious. The gap is real money: on a $1 million portfolio, 4% is $40,000 in the first year, where Bengen’s newer 5% to 5.5% would be $50,000 to $55,000. We plan on the smaller number on purpose, so that if anything, the plan understates the income these portfolios could sustainably produce.Balanced (≈ 50/50) stock/bond portfolio; first-year withdrawal then adjusted for inflation annually. Based on Bengen (1994) and the Trinity Study (1998). Past performance does not guarantee future results.In the case studies that follow, the “4% income” columns show this first-year withdrawal at each possible starting age. Because a Roth’s withdrawals are entirely tax-free, that 4% is money in hand, with no further tax due, and, by the rule’s own logic, is designed to last a full 30-year retirement and then some.✦Coming next: 2 · Why Hold It in a Tax-Advantaged AccountA NOTE FROM THE AUTHORStart Now is free to read and free to share. A new part publishes free every Sunday. Subscribe to get each part in your inbox as it goes out.If you find that it helps you, the kindest thing you can do is subscribe and pass it to one person who needs it.If you’d like to give back, pay it forward: donate any amount to a cause you believe in. I don’t collect a penny of it; it goes straight to the charity you choose, not to me. 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