# How money grows > Why time beats talent, and what you're actually buying when you invest. A free course from Learnfold. 6 lessons, 20–30 min. Web: https://learnfold.app/learn/money/ ## What you'll learn Explain why starting early matters more than saving a lot, and which choices quietly help or hurt your money over decades. ## Before you start No finance background needed. If you can multiply, you can follow every example. ## Outline ### Chapter 1: The math of time See growth build on itself, estimate doubling times in your head, and watch inflation eat idle cash. 1. [Growth on top of growth](https://learnfold.app/learn/money/compounding/): Why a small sum started early can match a big sum started late. 2. [The rule of 72](https://learnfold.app/learn/money/rule-of-72/): Work out how long money takes to double, in your head. 3. [Why cash quietly shrinks](https://learnfold.app/learn/money/inflation/): Inflation, real returns, and the job cash is actually good at. ### Chapter 2: What you actually own Learn what stocks and bonds are, why owning everything beats picking winners, and how to sit still when prices fall. 4. [What stocks and bonds are](https://learnfold.app/learn/money/stocks-and-bonds/): Owning a slice of a company versus lending money for a fixed return. 5. [Buy the haystack](https://learnfold.app/learn/money/index-funds-and-fees/): Why owning the whole market beats most stock pickers, and what a 1% fee really costs. 6. [When prices fall](https://learnfold.app/learn/money/when-prices-fall/): Volatility, loss aversion, and why selling in a panic costs so much. ## Lessons ## 1. Growth on top of growth Put \$1,000 somewhere that grows 6% a year. After one year you have \$1,060. In the second year you earn 6% on \$1,060, so you gain \$63.60 instead of \$60. That extra \$3.60 looks like nothing. It is also the whole idea of this course. When growth starts earning its own growth, that's compounding. In the early years it barely shows. Later it does most of the work. ### Before the numbers Every example in this course uses dollars, but the math works the same in any currency. The returns are illustrations, not forecasts. Past returns don't guarantee future ones, and this course is general education, not personal financial advice. ### Two savers Maya starts at 25. She puts \$200 a month into investments that grow 6% a year after inflation. At 35 she stops adding money for good and leaves the account alone. She has put in \$24,000. Sam waits until 35. Then he puts in \$200 a month, every month, until he turns 65. He puts in \$72,000, three times as much as Maya. | Saver | Years adding money | Total put in | Worth at 65 | | --- | --- | --- | --- | | Maya | 10 | \$24,000 | about \$187,000 | | Sam | 30 | \$72,000 | about \$195,000 | Sam pays three times as much and only just comes out ahead. Maya's money had an extra decade to compound, and over her last ten years her balance grows by more than \$80,000 without her adding a cent. "After inflation" means these figures are in today's money. A later lesson explains why that matters. ### Try it The calculator below adds the same amount every month and grows it at the yearly rate you pick. Gray is what you put in. Green is growth. Start with the defaults, then drag Years from 30 to 40 and watch the green. With \$200 a month at 6% for 30 years, you put in \$72,000 and end with about \$195,000. Stretch it to 40 years and you put in another \$24,000, yet the total jumps to about \$382,000. Those last ten years compound on the biggest balance you've ever had. Now go back to 30 years and double the monthly amount to \$400. The result doubles too, to about \$390,000. Doubling the money doubles the result. Adding years multiplies it. Leave the fee button alone for now. Its lesson comes later. Turn the surface and move the orange dot. Doubling the monthly deposit doubles the height at any year, while extra years follow the upward bend. ### What to take from this The amount you can set aside at 22 may feel too small to bother with. Its size matters less than its head start. A modest sum started young can rival a much bigger one started late, and the years are the one input you can't buy back. ### Rabbit holes > Why does compounding look like almost nothing for the first ten years? > If Maya had kept adding \$200 a month until 65, how much would she have? > How does compounding work on loans and credit card debt? Read online: https://learnfold.app/learn/money/compounding/ ## 2. The rule of 72 How long does money take to double? Divide 72 by the yearly growth rate. That's the whole rule. | Growth per year | 72 divided by the rate | Actual doubling time | | --- | --- | --- | | 3% | 24 years | 23.4 years | | 6% | 12 years | 11.9 years | | 8% | 9 years | 9.0 years | | 12% | 6 years | 6.1 years | Close enough to do on a walk, with no calculator. Try 6%, then 24%. The blue estimate stays close, but the purple exact answer shows where the shortcut drifts. ### Doublings stack The rule gets interesting when you count doublings. At 6%, \$10,000 becomes about \$20,000 after 12 years, \$40,000 after 24, and \$80,000 after 36. Look at what each doubling adds. The first adds \$10,000. The third adds \$40,000. Each doubling adds more than all the earlier ones put together. That's why cutting a timeline short hurts so much. The years you lose come off the end, where the doublings are biggest. It also explains why a small difference in rate turns into a big difference in money. Over 36 years, 4% a year doubles your money twice, so you end with 4 times what you started with. At 8% it doubles four times, and you end with 16 times. Twice the rate, four times the result. ### Why 72 The exact answer takes logarithms. For very small rates the magic number is closer to 69, and at the rates people usually care about, 72 lands close. It also divides evenly by 2, 3, 4, 6, 8, 9, and 12, which is the real reason people use it. The rule drifts at high rates. At 24% it says 3 years, and the real answer is a little over 3. ### It works against you too Anything that compounds follows the rule, including things that cost you. - Credit card debt at 24% a year doubles in about three years if none of it is paid off. - Prices rising 3% a year double in about 24 years, which means cash buys half as much. The next lesson is about this. - Fees compound against you as well. They get their own lesson in the next chapter. ### Try it in your head At 9%, how long does money take to double? 72 divided by 9 is 8 years. How much does money grow in 40 years at 6%? It doubles every 12 years, so that's three and a third doublings. Two, four, eight, and a bit more. Roughly ten times what you started with. The exact figure is 10.3. Once this clicks, you'll start doing it everywhere. A loan rate, a pay rise, a headline about prices. Divide 72 by the number and you know how fast it doubles. ### Rabbit holes > How do I flip the rule of 72 to find the rate I'd need to double my money by a certain age? > Why does the rule of 72 get less accurate at very high rates? > How long would it take a country's economy to double at 2% growth versus 7%? Read online: https://learnfold.app/learn/money/rule-of-72/ ## 3. Why cash quietly shrinks Hide \$1,000 under a mattress for ten years. You'll still have \$1,000 when you lift the mattress. It just won't buy as much. Inflation is the general rise in prices over time. If prices rise 3% a year, something that costs \$100 today costs about \$134 in ten years. Your \$1,000 then buys what \$744 buys now. Nobody took anything from you, and you still lost a quarter of your money. Press Play to watch buying power shrink, or scrub through the years. Set inflation to zero to see why the loss comes from rising prices. ### How fast it eats The rule of 72 works here too. At 3% inflation, prices double and cash loses half its buying power in about 24 years. Many central banks aim for around 2% a year, but they don't always hit it. Plenty of countries saw inflation above 7% in 2022, and some live with far higher rates for years. At 7%, cash loses half its value in about a decade. ### Nominal and real The number on your statement is the nominal return. What you can buy with it depends on the real return, which is growth after inflation. A rough way to get it is to subtract inflation from the nominal return. | Where the money sits | Nominal return | Inflation | Real return | | --- | --- | --- | --- | | Cash under the mattress | 0% | 3% | about -3% | | Savings account | 2% | 3% | about -1% | | Long-term investment | 9% | 3% | about 6% | That's why the first lesson said "6% a year after inflation." Real returns let you think in today's money. When the calculator shows about \$195,000 after 30 years, that's what it would buy at today's prices. The statement in 30 years would show a bigger number, and it would buy the same. Watch out for this when you read about investing. A fund that "returned 8%" in a year with 6% inflation made you about 2% richer. ### So is cash bad? No. Cash is the right home for money you'll need soon, like rent, an emergency fund, or a deposit you'll pay next year. Its job is to be there, at full value, on the day you need it. Investments might be down 30% that day. A common rule of thumb is that money you'll need within about five years shouldn't depend on the stock market. The mistake is leaving long-term money in cash because it feels safe. It does feel safe, and it's almost guaranteed to lose a little every year. Over decades, a little adds up. At 3% inflation, \$10,000 kept in cash for 30 years buys what about \$4,100 buys today. So split your money by when you'll need it. Short-term money sits in cash and accepts a small, steady loss. Long-term money goes somewhere it can outgrow prices. What that somewhere is comes next. ### Rabbit holes > Why do central banks aim for a little inflation instead of none? > Who wins and who loses when inflation suddenly jumps? > What happened to people's savings during hyperinflation in Weimar Germany? Read online: https://learnfold.app/learn/money/inflation/ ## 4. What stocks and bonds are Investing sounds abstract. Most of it comes down to two deals. You own part of something, or you lend money to someone. ### A stock is a slice of a company A company can be split into millions of equal pieces called shares. Buy one and you own a sliver of the business, including its buildings, its profits, and its future. If a company has 10 million shares and you hold 100, you own one hundred-thousandth of it. Your share can make you money in two ways. Some companies pay part of their profits to shareholders as dividends. And if the business grows more profitable, other people will pay more to own a piece of it. Over many years, share prices tend to follow profits. Over a few months, they follow mood. Nobody promises you anything. If the company struggles, the price falls. If it goes bust, shareholders are paid last, after lenders and suppliers, and often get nothing. ### A bond is a loan Buy a bond and you're lending money to a government or a company. They agree to pay interest on a schedule and return your money on a set date. A \$1,000 ten-year bond paying 4% gives you \$40 a year for ten years, then your \$1,000 back. Move to year 10 to separate the last interest payment from the returned principal. Change the coupon to see which payments change. Bonds are calmer than stocks because the payments are spelled out in advance. Calm isn't the same as safe. The borrower can fail to pay. And when interest rates rise, older bonds that pay less become less attractive, so their prices drop. In 2022, as rates climbed fast, many high-quality bond funds lost more than 10%, one of their worst years on record. ### Why anyone owns stocks at all Stocks swing much more than bonds, so investors only hold them if they expect a bigger reward. Over long periods, that reward has shown up. Studies of markets in many countries since 1900 put the average return on stocks at roughly 5% a year after inflation, and government bonds at a little under 2%. Averages hide a lot. Some countries did much better than 5%. In a few, like Russia after 1917, stock investors lost everything. And there have been stretches of ten years or more when stocks did worse than bonds. The higher expected return is real, and it comes with long, uncomfortable waits. ### Mixing the two Many investors hold both. Stocks do most of the growing. Bonds steady the ride, and when stocks crash they give you something that hasn't crashed to spend from. A common pattern is more stocks when you're young and the money won't be touched for decades, then more bonds as the day you need it gets closer. Most people don't buy single stocks or bonds directly. They buy funds, which pool money from many investors and hold hundreds or thousands of stocks or bonds at once. Which kind of fund turns out to matter a lot, and that's the next lesson. ### Rabbit holes > Why would anyone lend money to a government for 30 years at a fixed rate? > What actually happens to my shares when a company goes bankrupt? > Why did bonds fall so hard in 2022 if they're supposed to be the safe part? Read online: https://learnfold.app/learn/money/stocks-and-bonds/ ## 5. Buy the haystack Finding the next great company sounds like the smart move. The evidence says most people, professionals included, do better by owning all of them. ### Most stocks are duds The finance professor Hendrik Bessembinder studied every US stock from 1926 to 2016. Four out of every seven did worse over their lifetime than short-term government bills, which is roughly what cash earns. Just over 4% of companies produced all of the stock market's net gains. So the market's return comes from a small number of huge winners, and nobody knows in advance which ones they'll be. Hold ten stocks and you'll probably miss them. Hold thousands and you're sure to own them. Spreading your money this way is called diversification. Famous companies do go bust, and when you own a few thousand, one collapse barely shows. Compare one stock per basket with 30, then press Play. In this simplified model, spreading company risk narrows the paths, while shared market shocks still move every basket. ### Index funds An index fund buys every company on a list, called an index, in proportion to its size. It doesn't try to beat the market. It tries to match it, and because there's no team of analysts to pay, broad index funds often charge 0.2% a year or less. An actively managed fund pays people to pick stocks they think will beat the market. That research costs money, and active fees of around 1% a year are common. ### What the scorecards say S&P Dow Jones Indices publishes yearly SPIVA reports comparing active funds with the indexes they try to beat. Over 15-year periods, close to nine in ten actively managed US large-company funds have trailed their index. Reports for Europe, Canada, Australia, and other markets show a similar pattern, though the exact numbers vary. Some managers do win. The trouble is spotting them ahead of time, because last decade's winners rarely stay on top. The economist William Sharpe explained why in 1991, and it's plain arithmetic. Index investors as a group earn the market return, minus small fees. Everyone together owns the whole market, so active investors as a group must also earn the market return before costs. Their costs are higher, so on average they have to come out behind. ### What a 1% fee really costs A 1% fee sounds tiny. But it comes out every year, from your whole balance, including all the growth from earlier years. So it compounds, against you. Compare a 0.2% fee with 1%, then extend the years. The gap includes both the fees and the growth those fees could have earned. Go back to the calculator in Growth on top of growth and tap the fee button. With \$200 a month at 6% for 30 years, the final balance drops from about \$195,000 to about \$161,000. The fee takes about \$33,500, more than a quarter of your growth. Over 40 years it takes about \$89,000, close to a third. Most things in investing are out of your hands. You can't choose next year's return. You can choose what you pay, and you know that number before you start. ### Rabbit holes > If index funds just copy the market, who keeps stock prices sensible? > Why do last decade's best fund managers so rarely stay on top? > Where do I find every fee I'm paying on a fund, including the hidden ones? Read online: https://learnfold.app/learn/money/index-funds-and-fees/ ## 6. When prices fall Everything so far assumes you keep investing through the bad years. That's the hard part. The math takes an afternoon to learn. Sitting still while your balance drops can take years to learn. ### Falls are normal Volatility means how much prices swing, and stocks swing a lot. A drop of 10% or more at some point in the year is common, even in years that end with a gain. Big falls are rarer and much scarier. - From late 2007 to early 2009, US stocks lost more than half their value and took several years to get back to their old peak. - In early 2020, as the pandemic spread, stocks fell about a third in roughly a month, then recovered to a new high within six months. - Japan's stock market peaked in 1989 and took 34 years to reach that level again. The last one is a good reason to own companies from many countries, so no single market can hold you hostage for decades. ### Why people sell at the bottom In experiments, a loss hurts roughly twice as much as an equal gain feels good. The psychologists Daniel Kahneman and Amos Tversky called this loss aversion. When your balance falls by \$20,000, every instinct says get out before it gets worse. Selling feels like taking control. Here's the trap. Selling turns a temporary drop into a permanent loss. Then you have to decide when to get back in, and most people wait until it feels safe, which usually means after prices have recovered. They sell low and buy high, the exact opposite of the plan. The market's best days also tend to arrive close to its worst ones, so people who jump out often miss the rebound. Try a 50% fall and a 50% rebound. A gain applies to the smaller balance, so getting back to the start requires 100%, and no rebound is assured. This shows up in real money. Morningstar compares what funds returned with what their investors actually earned, given when they bought and sold. Investors usually earn less than the funds they own. In its recent US studies, the gap has been a little over one percentage point a year. You know by now what 1% a year does over 30 years. ### How people stay put - Only invest money you won't need for years. If rent depends on it, a crash forces you to sell. - Keep an emergency fund in cash, so losing a job doesn't mean selling shares at the worst time. - Invest the same amount automatically each month. When prices are down, your \$200 buys more shares. - Check less often. Daily prices are mostly noise, and every look is a chance to panic. - Decide your mix of stocks and bonds while you're calm, and write down why. If you're adding money every month for decades, a crash in your twenties isn't a disaster. You spend years buying at lower prices. The person who gets hurt is the one who sells. That's the end of the course. The rabbit holes below go deeper, and you can fork any sentence on any page into a new one. ### Rabbit holes > How long did it really take investors to recover after the 1929 crash? > Why does checking my portfolio more often make me more likely to sell? > What is rebalancing, and does it help during a crash? Read online: https://learnfold.app/learn/money/when-prices-fall/ --- Read this course in the Learnfold app to ask about any sentence, follow a question into a new lesson, or have it rebuilt around what you already know: https://apps.apple.com/us/app/learnfold/id6794672797