How does compound interest actually work?
Compound interest pays interest on interest already earned, so the balance grows on a curve rather than a line. At 8% a year, money doubles roughly every nine years — and doubles again every nine years after that.
Updated 2026-08-22
The difference from simple interest
Simple interest is calculated only on the original amount. Put 10,000 somewhere paying 8% simple interest and you receive 800 a year, every year, for as long as it sits there. After thirty years you have earned 24,000 and the balance is 34,000. The growth is a straight line.
Compound interest is calculated on the balance, which includes interest already added. The first year still pays 800. The second year pays 8% of 10,800, which is 864. The third pays 8% of 11,664. Each year the base is larger, so each year pays more than the last, and the growth is a curve.
Over thirty years at 8%, that same 10,000 becomes about 100,600 rather than 34,000. The rate is identical and the starting amount is identical. The entire difference — roughly 66,000 — comes from interest earning interest.
What makes this counterintuitive is that the two look almost the same at the start. After one year they are identical. After five years compounding is ahead by about 700, which on 10,000 is not dramatic. The gap only becomes obvious in the last third of the period, which is exactly the part people are least able to imagine when deciding whether to start.
Slow, then sudden
The most useful mental model is doubling. At a given rate, money takes a fixed length of time to double, and then the same length again to double from there. The rule of 72 estimates it: divide 72 by the annual percentage rate and you get the years to double. At 8%, that is nine years.
Follow it through. After nine years, 10,000 is 20,000. After eighteen, 40,000. After twenty-seven, 80,000. After thirty-six, 160,000. The amount added in the fourth doubling — 80,000 — is more than the total balance after twenty-seven years of the first three. Nothing changed about the rate; the base simply got large.
This is why the single most important variable in long-term compounding is not the rate but the time. An extra percentage point helps. An extra decade helps far more, because it is the last doubling that carries the most absolute weight, and you only reach it by starting early enough to get there.
It also explains why compounding feels disappointing for years. Someone who has been saving diligently for five years and sees a modestly larger balance is looking at the flat part of a curve they have not yet noticed is a curve. The arithmetic has not failed; the interesting part is genuinely later.
Frequency, and why it matters less than you think
Interest can be compounded annually, monthly, daily or continuously, and more frequent compounding does produce a larger result — but the effect is much smaller than the headline suggests.
Take 10,000 at 8% for one year. Compounded annually it becomes 10,800. Monthly, 10,830. Daily, 10,832. Continuously — the mathematical limit — 10,833. The step from annual to monthly is worth 30; every further increase in frequency is worth almost nothing. The curve of benefit flattens fast.
This is what the distinction between a nominal rate and an effective rate is for. A card advertising 18% compounded monthly has an effective annual rate of 19.6%, because each month's interest joins the balance the next month charges on. Comparing a monthly-compounded product against an annually-compounded one at their nominal rates is comparing two different things, and the effective rate is what makes them commensurable.
The practical advice is to compare effective rates and then stop thinking about frequency. Between two accounts, the rate and the fees will decide the outcome; the compounding interval almost never will.
Adding money as you go
Most real saving is not a lump sum left alone. It is a smaller amount added every month, and that changes the shape of the result in a way worth understanding, because the two effects pull in different directions over time.
Each contribution starts its own compounding clock. Money paid in during the first year has the full period to grow; money paid in during the final year has almost none and contributes roughly its face value. So an early contribution is worth several times a late one, even though both are the same amount out of the same account.
The practical consequence is that the balance is dominated by contributions in the early years and by growth in the later ones. At the start, almost everything in the account is money you put there. Somewhere along the way the accumulated growth overtakes the total contributed, and from that point the account is mostly earning rather than being fed. Reaching that crossover is the real reason starting early matters more than contributing heavily.
It also means a contribution missed early is not equivalent to one missed late. Skipping a year of saving at the beginning removes an amount that would have doubled several times; skipping the same year at the end removes roughly what it was. That asymmetry is invisible if you only look at the total paid in, which is why two people who contributed identical amounts can finish with very different balances.
The same curve, pointed at you
Everything above works identically on debt, and this is the half that gets less attention. A credit card at 22% doubles what you owe in a little over three years if nothing is paid. The balance grows on precisely the same accelerating curve, and the minimum payment is often set close to the interest charge, which is why a balance can be serviced for years and barely move.
Inflation is the third version of the same arithmetic. At 6%, prices double in about twelve years, which is a far more legible statement than the percentage. Money sitting in an account paying 2% during 6% inflation is losing about 4% of its purchasing power a year, compounding — a positive number describing a real loss.
Fees compound too, and against you. A fund charging 1% a year does not cost you 1% of your final balance; it costs you 1% of the balance every year, including the growth that money would have produced. Over thirty years, a one-point difference in fees typically consumes something in the region of a quarter of the final amount. That is why fee comparison matters far more than it appears to when the numbers are small.
The rule of 72 is the fastest way to make any of these concrete. Whatever rate you are looking at — savings, debt, inflation, fees — divide 72 by it and you have the number of years until it doubles. That single division converts an abstract percentage into something you can actually reason about.