Compound Interest: The Math Behind Long-Term Wealth

Simple interest pays a fixed return on the original principal each period. At 5% simple interest, $10,000 earns $500 a year; after 20 years that is $10,000 of interest, for a total of $20,000.

Compound interest pays returns on the whole accumulated balance. At 5% compounded annually, $10,000 grows to $10,500 after one year and to $11,025 after two (5% of $10,500, not of $10,000). After 20 years the balance is about $26,533, against $20,000 with simple interest. The $6,533 difference is interest earned on interest.

The formula is Final value = Principal × (1 + rate)^years. At 8% for 30 years the multiplier is 1.08³⁰, about 10.06, so $10,000 becomes about $100,627 without further contributions.

Dividing 72 by an annual return in percent gives the approximate number of years it takes money to double. At 4%, that is about 18 years (the exact figure is 17.7). At 8%, about 9 years. At 10%, about 7.2 years (exactly 7.3). The rule is most accurate between about 6% and 10%.

It works for inflation too. At 3% annual inflation, the purchasing power of cash halves in about 24 years; at 7%, in about 10. From 1970 to 1980, when consumer prices rose an average of 7.8% a year, a dollar held as cash lost 53% of its purchasing power.

Time in the market often matters more than a higher return. Investor A puts $10,000 in at age 25 and earns 7% a year. Investor B invests the same $10,000 at age 35 and earns 9% a year. At 65:

Investor A: $10,000 at 7% for 40 years = $149,745.
Investor B: $10,000 at 9% for 30 years = $132,677.

Investor B earns two percentage points more every year and still finishes about $17,068 behind, because A's first ten years of growth are compounded for another thirty.

The same arithmetic prices a delay. At 8% a year, starting five years later leaves the final balance about 32% smaller for the same end date, since the money compounds for five fewer years.

Over 1928–2025, the S&P 500 returned about 10% a year with dividends reinvested, according to annual return data compiled by NYU's Aswath Damodaran, while consumer prices rose about 3.0% a year.

Dividends make a large difference over long periods. $10,000 invested at the end of 1990, when the index closed at 330.22, would have grown to about $207,301 by the end of 2025 on price changes alone, roughly 9.0% a year. With every dividend reinvested, the same $10,000 grew to about $400,600, roughly 11.1% a year, before fees and taxes. Reinvested dividends and the returns they earned account for about 48% of that ending balance, even though the dividend yield in any single year was only a few percent.

On price alone, the same $10,000 from the end of 1990 was worth about $234,492 at the latest reading (September 25, 2026).

Fees compound too. A fund charging 1% a year takes 1% of the balance every year, so that money and everything it would have earned are gone from all later years.

Treating the fee as a cut in the annual return, $10,000 at 8% for 30 years grows to about $100,627. At 7% (an 8% return less a 1% fee), it grows to $76,123: the fee costs about $24,504, roughly a quarter of the fee-free result. At a 1.5% fee the balance is about $66,144, about a third less.

Fund costs have fallen. The Investment Company Institute reports that the asset-weighted average expense ratio for equity mutual funds was 0.40% in 2024, down 62% since 1996, and 0.14% for index equity ETFs. Over 30 years at 8%, the difference between a 0.05% and a 1% annual cost on $10,000 is about $23,116.

Account balances compound in nominal dollars, but what the money buys depends on the real return, after inflation. The real rate is (1 + nominal) ÷ (1 + inflation) − 1: a 10% return with 3% inflation is a real return of about 6.8%, not 7%.

$10,000 compounding at 10% for 30 years reaches about $174,494. With 3% inflation over the same 30 years, that balance buys what about $71,889 buys today, about 41% of the nominal figure. Planning in real dollars gives a more accurate picture of what a long-term investment will pay for.

The examples above compound once a year. Many savings accounts compound monthly or daily, which earns slightly more at the same stated rate: 5% compounded daily is an annual percentage yield (APY) of about 5.13%. Compounding more often than daily adds almost nothing further. Under the Truth in Savings Act, US banks must quote the APY, which already includes the effect of compounding frequency.

Compare savings products by APY rather than stated rate. Between a savings account and an investment, the frequency matters far less than the rate: on $10,000 over ten years, daily rather than annual compounding at 5% adds about $198, while a rate one point higher adds about $1,620.