Interactive lesson
Compound interest: why time beats timing
Guess, slide, sort and draw your way to the most useful idea in money: growth on growth. Then test it on US stocks since 1871.
Look
Money that makes money
Put $1,000 to work at 7.1% a year — the pace of US stocks after inflation since 1871. Year one earns $71.09. Year two earns 7.1% on the bigger sum, so the interest earns interest too. That is compounding. After 30 years, interest on interest alone comes to $4,716, more than double the plain interest of $2,133.
Guess
Thirty years later
$1,000 grows 7.1% a year for 30 years. What is it worth at the end?
Show the answer
$7,848. Straight-line thinking adds $71.09 a year and lands at $3,133. Compounding makes it $7,848, 7.85 times the start — and 69% of the gain is interest earned on interest.
Explore
Time is the lever
Move the sliders. The dashed line is simple interest: what you would get if interest never earned interest.
At 7.1% a year, you double the time from 20 to 40 years. The final sum becomes…
- Twice as big
- About 3.9 times as big
- Ten times as big
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About 3.9 times as big. $3,949 after 20 years, $15,597 after 40. The second 20 years multiply by the same 3.9 as the first — on a much bigger base.
Pick one
The rule of 72
A pocket shortcut: 72 divided by the yearly rate gives the years it takes money to double. At 8% a year, about how long is that?
- 6 years
- 9 years
- 12.5 years
- 18 years
Show the answer
9 years. 72 ÷ 8 = 9. The exact figure is 9.01 years: the rule is very close for rates from about 4% to 12%. At the stock market’s 7.1% after inflation the rule says 10.1 years; exactly, 10.1.
Put in order
Early or long?
Four savers each put $1,000 a year into stocks growing 7.1% a year after inflation, and leave it there until 65. Rank them by what they have at 65, most first.
- Bob saves 30 years, from age 35
- Alice saves 10 years from age 25, then stops
- Dan saves 20 years, from age 45
- Carol saves 40 years, from age 25
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- Carol saves 40 years, from age 25 — $219,929
- Alice saves 10 years from age 25, then stops — $116,747
- Bob saves 30 years, from age 35 — $103,183
- Dan saves 20 years, from age 45 — $44,436
Alice put in a third of Bob’s money and ends with more than Bob: $116,747 against $103,183. Her ten early years had 30 more years to compound. Carol, who did both, has $219,929.
Guess
The quiet thief
In Oct 1996 you hide $1,000 in a drawer. Thirty years later you take it out. US prices rose 2.5% a year in between. What does it buy now, in the money of 1996?
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$471. Prices rose 2.12 times, so the $1,000 buys what $471 did in 1996: 53% of its value gone, quietly. Inflation compounds too — against cash.
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Growth after inflation
Your money has to outrun prices. Set a return as quoted and an inflation rate: the solid line is what $1,000 grows into in today’s money.
Since 1871 US stocks returned 9.4% a year as quoted, and prices rose 2.1% a year. What did stocks return after inflation?
- 11.7%
- About 7.1%
- 9.4%
Show the answer
About 7.1%. Roughly the return minus inflation (7.3%); exactly, (1 + 9.4%) ÷ (1 + 2.1%) − 1 = 7.1%.
Draw it
Draw the last 30 years
Here is $1,000 put into US stocks in Oct 1996, counted after inflation. Draw how you think it went, year by year, to Oct 2026.
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1996 $1.0K 2001 $1.47K 2006 $1.78K 2011 $1.56K 2016 $2.88K 2021 $5.74K 2026 $8.77K It ended at $8,774: 7.5% a year, close to the long-run 7.1%. Smooth it was not: from Aug 2000 to Mar 2009 it lost 52%, and it took until May 2013 to get back. Those who stayed invested got the whole 30 years.
Pick one
Time or timing?
Two savers put $1,000 into the S&P 500 every year until 2025. Unlucky starts in 1986 and always buys in the year’s most expensive month. Lucky waits until 1996, then always buys in the cheapest month. Who has more today?
- Unlucky, who started early
- Lucky, the perfect timer
- About the same
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Unlucky, who started early. Ten extra years of growth beat thirty years of perfect timing: $623,285 against $245,241. Unlucky put in $40,000 and has $623,285; Lucky put in $30,000 and has $245,241. Over the same 1996–2025 stretch, perfect timing beat the worst timing by only 23%.
Look
A real check: every 30 years since 1871
Each bar is $1,000 put into US stocks in January of one year and left alone for 30 years, after inflation. The worst start, 1892, still grew to $2,599 (×2.6); the best, 1932, to ×18.6; the middle one ×7.36. Not one of the 126 stretches lost money.
Done
- Compounding is growth on growth: $1,000 at 7.1% a year became $7,848 in 30 years, 7.85 times the start.
- The rule of 72: 72 ÷ the rate = years to double. At the stock market’s pace after inflation, about 10.1 years.
- Starting early beats saving more later: Alice’s ten early years beat Bob’s thirty later ones.
- Inflation compounds against cash: $1,000 kept since 1996 buys $471 today.
- Time beat timing: the unluckiest buyer who started ten years earlier ended with 2.5 times the perfect timer’s money.
Go deeper
How the numbers are made
- Stocks: the S&P Composite index (the S&P 500 since 1957) with dividends reinvested, monthly from Jan 1871 to Oct 2026; after inflation with the US consumer price index.
- The long-run rate, 7.1% a year after inflation, is the compound growth over that whole span. Every “at this rate” example uses it; actual years were anything but smooth.
- The four savers put $1,000 in at the start of each year they save. The timing savers put $1,000 in each year in the month with the year’s highest or lowest average price; their amounts are as quoted, not adjusted for inflation.
- No taxes, fees or trading costs.
- Source: Robert J. Shiller, Online Data (S&P Composite, dividends, CPI, 10-year Treasury rate).
- A lesson about how things work, not investment advice. Past returns do not guarantee future results.