Compound Interest Explained (With the Rule of 72)

Compound interest is the one piece of financial maths that genuinely changes behaviour once people see it. The idea is simple — you earn interest on your interest — but the consequences over decades are so large that they feel like a mistake the first time you run the numbers. They’re not.

Simple vs compound

With simple interest, you earn a fixed amount each year based only on what you originally deposited. $10,000 at 7% simple interest earns $700 every year: $17,000 after ten years, $24,000 after twenty.

With compound interest, each year’s interest is added to the balance, and next year’s interest is calculated on the new, larger balance. The same $10,000 at 7% becomes $19,672 after ten years and $38,697 after twenty. The gap between simple and compound is small at first and enormous later — that curve bending upward is what people mean by “the power of compounding.”

The formula for a lump sum:

A = P × (1 + r/n)^(n×t)

P is the starting amount, r the annual rate, n compounding periods per year, t years. The compound interest calculator handles this plus regular contributions and draws the curve.

The rule of 72

To estimate how long money takes to double, divide 72 by the annual return:

Return	Doubling time
3%	24 years
5%	14.4 years
7%	10.3 years
10%	7.2 years

It’s an approximation, but a good one between about 4% and 12%. It works in reverse too: if you need money to double in 9 years, you need roughly 8% a year. And it applies to costs as well as gains — at 3% inflation, prices double every 24 years; at 24% credit-card APR, an unpaid balance doubles every three.

Why starting early beats saving more

This is the example that changes minds. Two savers, both earning 7% a year:

• Alex saves $300 a month from age 25 to 35 — ten years, $36,000 total — then stops and never adds another dollar.
• Sam saves $300 a month from age 35 to 65 — thirty years, $108,000 total.

At 65, Alex has about $421,000. Sam has about $366,000. Alex contributed a third as much and ended up with more, because Alex’s money had thirty extra years to compound. The lesson isn’t “stop at 35”; it’s that the earliest dollars are the most valuable ones, so it’s worth starting with whatever you can rather than waiting until you can afford “enough.”

Regular contributions

Most people don’t invest a lump sum; they add a bit each month. The maths is the same, just applied to each deposit separately, and the effect is the same: early deposits do most of the work. Saving $500 a month at 7% for 30 years puts in $180,000 and ends with about $610,000 — more than two-thirds of the final balance is growth, not contributions.

The calculator shows a “contributed” line against the “balance” line; watching the gap open up is the clearest illustration of compounding there is.

Realistic rates

A rate is only useful if it’s honest. Rough historical guides for planning:

• High-yield savings and CDs: 3.5–5% in 2026, essentially no risk, fully compounding.
• Bonds: 4–6%.
• A diversified stock index fund: about 10% a year nominal over long periods, which is roughly 7% after inflation. Individual years swing wildly; the average only shows up over decades.

Use the after-inflation figure if you want to know what the money will actually buy. And note the rate’s leverage: over 30 years, 6% turns $10,000 into about $60,000 while 8% turns it into about $109,000. Fees that shave 1% off your return are, over a lifetime, a very large sum.

Compounding works against you too

Debt compounds exactly the same way. A $5,000 credit-card balance at 24% APR with only minimum payments takes over 20 years to clear and costs more than the original balance in interest. The fastest “return” most people can earn is paying off high-rate debt, because it’s a guaranteed 20%+ with no risk.

Three things to do with this

1. Open the compound interest calculator with a number you could actually save each month. Look at year 30. Then try starting five years later and look again.
2. If you’re paid hourly, the salary calculator tells you what a raise or a few extra hours a week is worth annually — often the easiest place to find the monthly contribution.
3. Automate it. Compounding needs time more than it needs skill; the only way to fail is to keep not starting.