Fundamentals
How compound interest actually works
Why money that earns money is the quiet engine behind every long-term plan — and the maths you can do on a napkin.
Simple interest pays you a fixed amount on your original deposit, year after year. Compound interest is different: each period you earn a return, that return is added to your balance, and the next period's return is calculated on the new, larger balance. You earn returns on your returns. That recursive loop is the whole idea, and it is why compounding looks unremarkable for years and then suddenly steep.
Here is the standard formula, stated plainly. A future value equals your principal multiplied by (1 + r) raised to the power of n, where r is the periodic rate and n is the number of periods. If you contribute regularly, each contribution starts its own compounding clock from the day it lands.
Time does the heavy lifting
Assume a steady 7% annual return — a common long-run stock-market assumption before inflation, not a promise. A single $1,000 left untouched becomes roughly $1,967 after 10 years, $3,870 after 20, and $7,612 after 30. Notice the gaps widen: the third decade adds far more dollars than the first, even though nothing about the deposit changed. The early years feel slow because the balance is small; the later years feel dramatic because the balance is large.
The practical lesson is unglamorous. A modest amount invested early can outpace a larger amount invested late, simply because it compounds for more years. Starting is usually worth more than optimising.
The Rule of 72, and its limits
To estimate how long money takes to double, divide 72 by the annual return expressed as a whole number. At 6%, doubling takes about 12 years; at 9%, about 8. It is an approximation that works best for rates between roughly 4% and 12%, and it ignores taxes and contributions. Treat it as a back-of-envelope sanity check, not a forecast.
Compounding cuts both ways
The same mechanism that grows savings also grows costs. A 1% annual fee does not cost you 1% — it costs you 1% of an ever-larger balance, every year, forgone-growth included. Over decades that can quietly subtract a meaningful share of your final balance. Inflation works similarly against purchasing power. Whenever you reason about compounding, reason in real, after-cost terms so the picture stays honest.
Common questions
- Is compound interest the same as compound growth?
- In everyday use, yes. 'Interest' usually describes cash savings and bonds, while 'growth' or 'returns' describes investments. The compounding mechanism — earning on your earnings — is identical. The difference is that investment returns are not guaranteed and can be negative in any given year.
- How often should interest compound to matter?
- More frequent compounding helps a little, but the effect is small compared with the rate and the time horizon. The gap between annual and daily compounding at the same stated rate is modest. Time invested and total cost matter far more than compounding frequency.
- Does the Rule of 72 work for any interest rate?
- It is most accurate for rates between about 4% and 12%. At very low or very high rates the estimate drifts. For precision, use the actual formula or a calculator rather than the shortcut.