Money & Finance › What money is & money theory › Interest: the rent paid for using money
Compound interest and the rule of 72
· Concept
Fact, law or dataA rule, statute, definition or measured number.
Compound interest earns interest on past interest, so money grows exponentially; the rule of 72 estimates the doubling time.
See it on the Money & Finance map →How it works
At 7% a year, $10,000 grows to about $19,700 in 10 years and about $76,000 in 30, versus $31,000 with simple interest. The rule of 72: divide 72 by the rate to get the years to double, so 8% doubles in about 9 years and 3% in 24. It cuts both ways: an unpaid credit card balance at 24% doubles in about 3 years, and 3% inflation halves purchasing power in about 24.
Why it matters
Time is the biggest driver of long-term wealth or debt. Small rate differences become large gaps over decades, in investments, fees and loans.
Think of it like
Like reinvesting a building's cash flow into more buildings: the income itself starts earning income.
Facts, rules and data
Plain mathematics: A = P(1 + r)^n. The rule of 72 appears in Luca Pacioli's 1494 math textbook, Summa de arithmetica.
Debates and risks
The famous line calling compound interest 'the eighth wonder of the world' is often credited to Einstein, but no source shows he said it.
Connections (2)
▸Interest: the rent paid for using money grows exponentially through Compound interest and the rule of 72Fact, law or data
The connection
When interest is added to the balance and itself earns interest, growth becomes exponential instead of linear. Over long periods the interest on interest dwarfs the original sum: at 7%, $10,000 earns $21,000 of simple interest in 30 years but about $66,000 compounded.
When and why
Known in Mesopotamia, where Old Babylonian math tablets ask how long a loan takes to double; formalized in Renaissance Italy.
How we know
Pure arithmetic; any loan amortization table or long-run brokerage statement shows it at work.
Debates and risks
Little is in doubt about the math; the open question is why people consistently underestimate exponential growth, a bias economists study.
▸Compound interest and the rule of 72 powers long-run returns in Index funds and passive investingFact, law or data
The connection
Index funds keep more of each year's return because fees are tiny, and that difference compounds. At 7% a year, $100,000 grows to about $761,000 in 30 years; at 6%, after a 1% fee, it grows to about $574,000. Reinvested dividends compound the same way. Bogle called it the tyranny of compounding costs.
When and why
Bogle made the argument from the 1970s on; the SEC illustrates fee drag in its 2014 investor bulletin on fees and expenses.
How we know
Plain arithmetic: fee savings are certain, while market returns are not. Fund cost data from ICI and Morningstar confirm the fee gaps.
Debates and risks
Future returns are unknown, so the dollar figures are illustrations; whether index returns near 10% a year will continue is debated.