How compound interest
actually works

Published August 15, 2026 · 8 min read

The one-sentence version

Compound interest is interest calculated on your original money and on all the interest that money has already earned. That second part is the whole idea, and it is the reason a balance that grows slowly for years can suddenly seem to accelerate.

Simple interest versus compound interest

Say you put $10,000 into an account paying 7% a year and leave it alone for 30 years.

With simple interest, you earn 7% of the original $10,000 every year. That is $700 a year, every year, forever. After 30 years you have earned $21,000 in interest, for a total of $31,000.

With compound interest, year two pays 7% on $10,700 rather than on $10,000. Year three pays 7% on $11,449. The base keeps growing, so each year's interest is larger than the last. After 30 years you have roughly $76,000 — more than double the simple-interest result, from exactly the same deposit and the same rate.

Notice the shape of that last column. After one year the difference is nothing. After ten years it is a few thousand dollars. After thirty it is larger than the entire simple-interest balance. Compounding does not feel like it is working for a long time, and then it does.

The formula

The standard expression is:

A = P(1 + r/n)^nt

• A — the final amount
• P — the principal, what you started with
• r — the annual interest rate as a decimal, so 7% is 0.07
• n — how many times per year interest compounds
• t — time in years

One thing this formula does not handle: recurring contributions. If you are adding money every month, which is what most people actually do, the math gets messier and is easier to run month by month than to solve in one line. That is how the calculator on this site does it.

How much does compounding frequency matter?

Less than people assume. Here is $10,000 at 7% for 20 years at different frequencies:

Going from annual to daily compounding adds about $1,800 over twenty years. Real, but small. Going from 7% to 8% over the same period adds roughly $8,000. And extending from 20 years to 25 years adds about $16,000. Rate and time move the needle far more than frequency.

The "effective annual rate" column is worth understanding on its own. It tells you what a nominal 7% actually becomes once compounding is included, which is how you compare two accounts quoting rates on different schedules.

Why starting early beats starting bigger

Consider two savers, both earning 7%:

• Anna invests $200 a month from age 25 to 35, then stops completely and never adds another dollar. Total contributed: $24,000.
• Ben invests nothing until 35, then puts in $200 a month from 35 until 65. Total contributed: $72,000.

At 65, Anna has roughly $260,000. Ben has roughly $234,000. Anna contributed a third as much and still ended ahead, because her early money had thirty extra years to compound.

This is the single most useful thing to understand about compounding, and the reason the answer to "when should I start" is almost always "sooner than you think."

The Rule of 72

A quick mental shortcut: divide 72 by your annual rate to estimate how many years it takes to double your money.

• At 6%, roughly 12 years
• At 8%, roughly 9 years
• At 10%, roughly 7.2 years

It is an approximation, not a formula, but it is accurate enough for mental math and it makes the cost of a lower return obvious.

Compounding works against you too

Credit card debt compounds by exactly the same mechanism, only you are on the other side of it. At 22% APR compounding daily, a $5,000 balance you never pay down becomes over $6,200 in a year and more than $15,000 in five.

This is why paying off high-interest debt is often the highest-return use of a dollar. A guaranteed 22% avoided is better than a hoped-for 7% earned.

What compounding cannot do

Every example on this page assumes a steady, unchanging rate. Savings accounts roughly work that way. Investments do not. A portfolio averaging 7% delivers that through a sequence of good and terrible years, and the order they arrive in matters — particularly if you are withdrawing money rather than adding it.

Treat compound interest math as a way to understand the mechanism, not as a prediction of your balance on a specific future date.

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