How compound interest works (with worked examples)

Compound interest is the simplest idea in finance with the least intuitive consequences: interest earns interest, and over enough time that second-order effect becomes the main event. This guide walks through the mechanics with concrete numbers — frequency, contributions, the Rule of 72, and the version of the story where compounding works against you.

The 10-second answer

With simple interest, $10,000 at 5% earns $500 every year, forever. With compound interest, each year's $500 joins the balance, so year two earns on $10,500, year three on $11,025, and so on. After 30 years simple interest gives $25,000; compounding gives about $43,200. The difference — eighteen thousand dollars on a ten-thousand-dollar start — is interest earned by interest.

Principal vs interest-on-interest

Early on, almost all growth comes from the rate applied to your original money, and compounding looks like a rounding error. The effect snowballs because every year's interest permanently raises the base. In the example above, the first decade of compounding adds about $6,300, the second about $10,300, and the third about $16,600 — same rate, same starting balance, accelerating gains. This is why "time in the market" gets repeated so often: the last decade of a long horizon does disproportionate work, and it can only exist if the first decade happened.

Compounding frequency: real but overrated

A 5% nominal rate yields exactly 5% compounded annually, about 5.12% compounded monthly, and about 5.13% compounded daily. Frequency matters — it is the entire difference between a nominal rate and an APY, as explained in APY vs APR — but the gains shrink fast: going from annual to monthly captures nearly all of the benefit, and daily adds only slivers more. When comparing accounts, an APY difference of a tenth of a percent outweighs any difference in compounding schedule.

Contributions and timing

Regular deposits change the picture more than any frequency tweak. $10,000 at 5% compounded monthly grows to about $16,470 in 10 years on its own; add $100 at the end of each month and it reaches about $32,000 — $22,000 of it contributed, $10,000 earned. Timing adds a final nuance: deposits made at the beginning of each period rather than the end spend one extra period invested, which compounds into a small but persistent advantage over long horizons.

The Rule of 72

Divide 72 by the annual rate to estimate doubling time: at 6%, money doubles in about 12 years; at 9%, about 8. Chain it for intuition — at 7%, a 40-year horizon holds roughly four doublings, so a dollar invested at 25 is on the order of $16 by 65. The rule is an approximation that is most accurate for single-digit rates, but it makes long-horizon claims easy to sanity-check without a spreadsheet.

When compounding works against you

Debt compounds by exactly the same arithmetic. Carry a $3,000 credit card balance at 22% APR and the unpaid interest joins the principal each month; an $80 minimum payment barely outruns the roughly $55 of monthly interest, which is how a balance can take a decade to clear. The asymmetry of rates does the damage: money saved at 5% doubles every 14 years, while debt at 22% doubles in under four. The debt payoff calculator shows what extra payments do to that timeline.

Run your own numbers

The compound interest calculator projects any combination of starting balance, rate, compounding frequency, contributions, and timing, and splits the result into what you put in versus what compounding added. To layer in fees and inflation, continue with the investment calculator.