How Compound Interest Works, and What Quietly Eats It

Compound interest is interest that earns interest. Put $1,000 into an account paying 5% a year and after twelve months you have $1,050. The second year's 5% is charged on that $1,050, not on the original $1,000, so you earn $52.50 instead of $50. That extra $2.50 is the entire mechanism. Leave the same $1,000 alone for 30 years and it becomes $4,322, against the $2,500 simple interest would have paid — and every dollar of the $1,822 difference is interest paid on interest.

What is the difference between simple and compound interest?

Here is that $1,000 at 5%, with nothing added and nothing withdrawn. Simple interest pays $50 a year forever. Compound interest pays 5% of whatever is in the account.

After five years the difference is $26 and you would be forgiven for not caring. Between year 30 and year 40 the compound column adds $2,718 while the simple column adds $500. Nothing changes in those last ten years except that the balance doing the earning is much bigger. That is the shape to remember: compounding is unimpressive for a long time and then it is not.

What is the compound interest formula?

The textbook version is FV = P × (1 + r/n)nt. P is what you start with, r is the annual rate as a decimal, n is how many times a year interest is added, and t is the number of years. For the example above: 1000 × 1.05³⁰ = 4,321.94.

That formula describes a lump sum left completely alone. It stops working the moment you pay money in regularly, which is what most people are actually asking about. More on that below.

Why is the quoted rate not the rate you get?

The n in that formula hides something. A bank advertising "6%" is usually quoting a nominal annual rate, and the amount you actually earn depends on how often it compounds. The effective rate is (1 + r/n)n − 1:

• Compounded yearly — exactly 6.00%
• Every six months — 6.09%
• Quarterly — 6.14%
• Monthly — 6.17%
• Daily — 6.18%

Notice how fast that flattens. Going from yearly to monthly buys you 0.17 percentage points. Going from monthly to daily buys under 0.02, and slicing finer than that changes almost nothing: compounded continuously, the same nominal 6% tops out at 6.1837%. An account advertising daily compounding is advertising its last two decimal places. The figure that already has all of this baked in is published as APY in the United States and as AER in the UK, and comparing two accounts on anything else is comparing the wrong number.

What happens when you contribute every month?

Almost nobody deposits a lump and walks away. Once you contribute every month, the neat formula is replaced by a series of deposits that each compound for a different length of time, and the arithmetic stops being something you do on the back of an envelope.

Say you pay in $250 a month at a nominal 6% compounded monthly. After 20 years the balance is about $115,500. You put in $60,000 of that; the other $55,500 is growth. The interesting part is the distribution. In the first year the account earns about $84 in interest. In the twentieth year it earns about $6,600 — more than double what you pay in over the same twelve months.

This is why savings plans feel pointless for the first five years and then stop feeling pointless. It is also why changing the numbers beats arguing about them: the savings growth calculator here walks the projection forward a month at a time and prints every year with the total you have paid in and the total growth side by side, so you can watch the second column close on the first instead of guessing. It also handles a contribution that rises a set percentage each year, which is closer to how most people actually save.

How long until the money doubles?

Divide 72 by the interest rate. At 6% a year, 72 ÷ 6 = 12 years, and the exact answer is 11.9. At 9% the rule says 8 years and the exact answer is 8.04. At 3% it says 24 and the truth is 23.4.

The rule of 72 is at its best somewhere around 8% and drifts at the extremes, but for a number you can do at a traffic light it is remarkably good. It works in the other direction too: something growing at 1% a month doubles in about six years, which is the kind of thing worth noticing on a subscription price. If doing that sort of percentage arithmetic in your head is the part that slows you down, the same tricks that make discounts easy to work out mentally apply here.

What eats into compound interest?

Every projection you have ever seen is a gross number. Three things stand between it and you.

Inflation. At 2% a year, money loses about a third of its purchasing power over 20 years. At 3% it loses nearly half. A balance that grows at 4% while prices rise 3% is growing at roughly 1% in the only terms that matter. The calculator shows a "today's money" column for exactly this reason — it is the difference between a projection and a fantasy.

Fees. Fees compound the same way returns do, which makes them far more expensive than they look. A 1% annual fee against a 7% return does not cost you 1%. Over 30 years it removes roughly a quarter of the final balance, because you are compounding at 6% instead of 7% the whole way.

Tax. Interest, dividends and capital gains are treated differently in every country, and differently again inside a tax-sheltered account. No general calculator can model this, including ours. If tax applies to you, the workaround is to enter a rate net of tax and net of fees rather than the headline return, and to read the result as an estimate.

Does compound interest work against you on debt?

Compounding is not a savings feature. It is arithmetic, and debt runs on the same arithmetic in the other direction.

A credit card quoting 20% APR and applying a daily periodic rate costs an effective 22.1% a year on any balance you carry. The symmetry is worth spelling out: money that clears a balance compounding at 22.1% has removed a certain 22.1% a year, while the same money in a savings account earns whatever that account pays — a different number, and usually a much smaller one.

Instalment loans are gentler but follow the same rule: interest accrues on what you still owe, so early payments go mostly to interest and late ones mostly to principal. Where the money in a loan payment actually goes covers that split, and a loan calculator will show you the schedule for your own numbers.

Why is a fixed-rate projection usually wrong?

Every calculator on this subject, ours included, assumes one rate repeated forever. Real returns arrive in an order, and once you are paying money in, the order is not a detail.

Take two decades, one returning 12% a year and one returning nothing, and run them both ways round. A $10,000 lump sum ends at $31,058 either way, because multiplying by the same set of numbers in a different order gives the same answer. Now pay in $250 a month across those same two decades instead. Good decade first ends near $85,500. Flat decade first ends near $148,700. Same $60,000 paid in, same twenty years of returns, and a gap of about $63,000 — because in the second run the contributions had piled up before the growth arrived.

That is the thing a single-rate projection structurally cannot show you, and it cuts both ways: a bad stretch early in a savings plan is cheap, and the same stretch just before you need the money is not. The other weak line is the one nobody audits. The largest error in most projections is not the return you picked; it is that you stopped paying in during year seven. Run the numbers twice, once at the rate you hope for and once two or three points below it, and the honest version of the answer sits somewhere between.

Last updated September 19, 2026