How Compound Interest Actually Works

One number is meaningless. Two are an argument.

$10,000 at 7% for 20 years grows to $40,387.

On its own that's just a big number. Put it next to the same money earning simple interest — where interest is paid only on the original sum and never on itself — and it becomes an argument:

Simple interest	$24,000
Compound interest	$40,387
The difference	$16,387

That $16,387 is interest that earned interest. It's 40% of the final total — more than the original $10,000 you put in.

The arithmetic

Compound: P × (1 + r/n)^(n × years)

10,000 × (1 + 0.07/12)²⁴⁰ = $40,387

Simple: P × (1 + r × years)

10,000 × (1 + 0.07 × 20) = $24,000

Compounding frequency barely matters

This surprises people, because it's the thing most often advertised.

Same $10,000, same 7%, same 20 years:

Compounded	Result
Annually	$38,697
Monthly	$40,387
Daily	$40,547

Annual → monthly is +4.4%. Monthly → daily is +0.4%.

The returns flatten out fast. A product advertising daily compounding isn't offering you a meaningfully different deal from one compounding monthly, and it's not worth choosing on.

What actually moves the answer, in order:

1. Time — the only input that compounds on itself
2. Rate — large, and the one people inflate
3. Starting amount — linear; twice the start is twice the end
4. Frequency — a few percent, total

The Rule of 72, and how good it is

Divide 72 by your interest rate to get an approximate doubling time.

At 7%: 72 ÷ 7 = 10.3 years. The real answer, worked out with logarithms: 9.93 years.

Close. It's reliably good roughly between 5% and 12%, and drifts at the extremes — reading a little short at very low rates and a little long at very high ones. The calculator does it properly so you can see the size of the gap for your own numbers.

Optimism compounds too

This is the part worth being careful about.

Assuming 10% instead of 7% roughly doubles a thirty-year projection.

That's not a small over-estimate you can absorb. It's a plan that fails quietly and late — at the point where there's no time left to correct it. The same mechanism that rewards patience punishes a hopeful rate just as efficiently.

Use a rate you can defend. If you're unsure, use the lower one. Savings accounts pay their stated APY; investment returns aren't a rate you get to choose.

What's missing from these numbers

Inflation, and over long periods it's not a technicality. A 7% nominal return with 3% inflation is roughly 4% in real purchasing power, and compounding that difference over decades gives a very different picture. If you want the answer in today's money, enter the real rate — expected return minus expected inflation.

Fees. A 1% annual fee comes straight off your return. Subtract it from the rate before you start.

Tax, unless the account is sheltered.

Contributions. This models a lump sum left alone, deliberately — it keeps the compounding effect visible rather than tangled up with new money arriving. For regular saving, the savings goal calculator answers what you need to put in each month to reach a target by a date.

The one thing to take away

Time is the only input that compounds on itself. Everything else is linear or nearly so.

Which is why "start earlier" beats "find a better rate" for almost everyone, almost always — and why the frequency on the advert is the least important number on the page.

Print the compounding reference.

General information, not financial advice. Investment returns are not guaranteed and past performance doesn't predict future results.