Compound interest explained: formula, rule of 72, examples

Compound interest is the only force in personal finance that works while you sleep, and it is worth understanding properly because every long-term number you will ever meet — retirement projections, savings goals, loan horror stories — is this one mechanism wearing different clothes.

The mechanism

Simple interest pays you on what you put in. Compound interest pays you on what you put in plus everything it has already earned. Each period, the base grows, so the next period's interest is bigger, and the curve bends upward. The formula behind every calculator:

FV = P × (1 + i)ⁿ + C × [((1 + i)ⁿ − 1) / i] — where P is what you start with, C is what you add each period, i is the per-period rate and n the number of periods.

A worked example, honestly labelled as illustration: 100 a month at 5% a year becomes roughly 15,500 after ten years — of which only 12,000 is money you put in. Extend to twenty years and the balance passes 41,000: the second decade adds more than twice what the first did, with identical contributions. That back-loaded shape is the entire point.

Time beats amount

Because n sits in the exponent, starting early outruns contributing more, later. A saver who puts in less for longer typically finishes ahead of one who puts in more for shorter — and the gap widens with every year of delay. This is why every retirement authority on earth gives the same one-line answer to “when should I start”: now, with what you have.

The rule of 72

The quick-and-dirty doubling time: 72 ÷ annual rate ≈ years to double. At 4%, money doubles in about 18 years; at 6%, about 12; at 8%, about 9. It is an approximation (exact doubling is a logarithm), accurate enough for planning and useless for precision — but it makes the exponential feel real, which spreadsheets oddly fail to do.

The same mechanism, pointed at you

Compound interest has no loyalty. On a credit card charging 20%+, minimum payments mostly feed interest, and the same exponential that builds a retirement fund builds a debt spiral — the rule of 72 says a 24% balance doubles in three years if unpaid. This is the arithmetic behind the avalanche debt method: high-rate debt is negative compounding, and it compounds faster than most investments can.

The honest caveats

Projections assume a steady rate; real returns fluctuate, and savings rates change with central banks. Inflation is the silent tax on nominal growth — 5% interest in a 4% inflation year is 1% of real growth, and in high-inflation environments the real rate can be negative, which changes the currency question, not the mechanism. And any product promising compounding at rates far above government bond yields is not offering you compound interest; it is offering you a story. The maths is dull, patient and reliable — which is exactly why nothing exciting ever beats it over twenty years.

Sources and further reading

Links were reviewed 2026-09-25. Regulatory permissions, firm status and product terms can change; use the current official register before acting.