Simple versus compound
Simple interest pays a fixed amount on the original sum forever. Compound interest pays on the growing balance. Over short periods the difference is trivial; over decades it is the whole result.
$10,000 at 8% for 30 years: simple interest returns $34,000. Compounded annually it returns $100,627 — nearly three times as much from the same rate.
The rule of 72
Divide 72 by the annual return to approximate the years needed to double your money. At 6% that is 12 years, at 9% it is 8 years, at 12% it is 6. It is a rough shortcut, and accurate enough to make the effect of a few extra percentage points immediately obvious.
Time beats contribution size
Because growth is exponential, the earliest contributions do disproportionate work — they have the longest to compound. Someone investing for ten years and then stopping frequently finishes ahead of someone who starts ten years later and never stops.
- $200/month from age 25 to 35, then nothing, at 8%: roughly $340,000 by 65.
- $200/month from age 35 to 65, at 8%: roughly $300,000 by 65.
- The first person contributed $24,000, the second $72,000.
Compounding works against you too
Debt compounds on exactly the same maths, which is what makes credit card balances at 20% so destructive. Fees compound as well: a 1% annual management fee does not cost 1% — over thirty years it removes a substantial share of the final balance, because every pound taken also stops compounding.