Simple vs compound, the difference that builds millionaires
Simple interest pays you only on your original deposit. Compound interest pays you on your original deposit plus all the interest that's already been added. Year one, the gap is invisible. Year 30, the gap is enormous. Compound growth is multiplicative; simple growth is linear.
Mathematically: with simple interest at 7%, $10,000 becomes $31,000 in 30 years. With compound interest at 7%, the same $10,000 becomes $76,123. Same rate, same time, more than double the result, just from letting prior gains earn their own gains.
The chart that makes 20-year-olds open a brokerage
Investor A starts at age 22, invests $200/month for 10 years (total contribution: $24,000), then stops contributing entirely. Investor B starts at age 32 and invests $200/month all the way to 65 (total contribution: $79,200). Both earn 7% real returns.
At age 65, Investor A, who contributed less than a third as much, finishes with about $345,000. Investor B finishes with about $300,000. The 10-year head-start mattered more than 33 years of catch-up contributions. Time, not money, is the dominant variable.
The Rule of 72
Divide 72 by your annual return to get the years it takes for money to double. At 7% returns, money doubles every ~10 years. At 10% returns, every ~7.2 years. This rule is not perfect arithmetic but it's accurate enough to do in your head and shockingly useful: a 30-year horizon at 7% means roughly three doublings, turning $10,000 into roughly $76,000, without adding a dollar.
A 1% improvement in return matters more than most savers realise. Going from 6% to 7% over 30 years grows a $100,000 portfolio from $574,000 to $761,000, a $187,000 difference, just from one percentage point.
What the curve looks like at year 5, 15, 25, 35
- Year 5: contributions are still the bulk of your balance. Returns feel small.
- Year 15: returns roughly equal contributions. The curve starts to bend.
- Year 25: returns dwarf contributions. The portfolio is doing more work than you are.
- Year 35: most of the balance is interest on interest. This is the 'eighth wonder' phase.
The three levers, and which one matters most
- Time, the single biggest variable; doubles your money roughly every 10 years at 7%. Start now even with $50/month.
- Rate of return, every 1% earned compounds itself. Low fees and broad equity exposure are the two known levers here.
- Contribution amount, matters most when time is short. After age 50, increasing contributions is the only lever still available.
Common compounding mistakes
- Waiting to invest until you 'have more money.' Time is the irreplaceable input.
- Cashing out a 401(k) when changing jobs, you don't just lose the balance, you lose 30 years of compounding on it.
- Holding too much cash for 'someday' decisions, every year in cash forfeits a year of compounding.
- Paying 1% in fund fees because the manager 'beats the market sometimes.' That 1% is your compounding being siphoned off.
How to use compound math against debt
Compounding is symmetric: it works against you on credit-card debt. A $5,000 balance at 24% APR with minimum payments takes ~22 years to pay off and costs roughly $7,400 in interest. The same $5,000 invested for 22 years at 7% becomes about $22,000. The opportunity cost of carrying high-interest debt is the missed compounding on what those payments could have grown into.
