What Is Compound Interest?
Compound interest means earning returns on your returns. Simple interest only earns on your original principal. Compound interest earns on the principal and on every dollar of interest previously earned. Over time, this creates an exponential curve — your money starts making more money than you do.
A = Final amount • P = Principal (starting amount) • r = Annual interest rate (decimal) • n = Compounding periods per year • t = Years
Simple vs Compound: The Difference Over 30 Years
$10,000 invested at 8% — simple vs compound:
| Year | Simple Interest | Compound Interest (Monthly) | Difference |
|---|---|---|---|
| 10 | $18,000 | $22,196 | $4,196 |
| 20 | $26,000 | $49,268 | $23,268 |
| 30 | $34,000 | $109,357 | $75,357 |
At year 10, the gap is modest. By year 30, compound interest produces 3.2× more than simple interest — $109K vs $34K. The gap accelerates because each year's interest earns interest the next year. This is the "snowball effect": a small snowball rolling downhill, picking up more snow with every rotation.
The Rule of 72
The fastest way to estimate how long it takes money to double: divide 72 by the interest rate.
| Interest Rate | Years to Double (Rule of 72) | Actual Years |
|---|---|---|
| 4% | 18.0 years | 17.7 years |
| 6% | 12.0 years | 11.9 years |
| 8% | 9.0 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6.0 years | 6.1 years |
The Rule of 72 is accurate within 3% for rates between 4-15%. At 10%, your money doubles every 7.2 years. Over 30 years, that's about four doublings — $10K → $20K → $40K → $80K → $160K. Compare that to 4% where your money doubles once every 18 years — just 1.7 doublings in 30 years.
Why Starting Early Beats Earning More
The most counterintuitive truth in investing: time matters more than rate. Two investors:
Early Emma (starts at 25, stops at 35)
Invests $5,000/year from age 25 to 35 (10 years, $50K total), then stops entirely. At 8%, the $50K grows to $602,000 by age 65.
Late Larry (starts at 35, never stops)
Invests $5,000/year from age 35 to 65 (30 years, $150K total) at 8%. Final balance: $540,000.
Emma invested $50K and ended with $602K. Larry invested $150K — 3× more — and ended with $540K. Emma wins by $62,000 despite investing $100K less. Her money had 10 extra years to compound. Those 10 years were worth more than Larry's extra $100K in contributions.
How Fees Destroy Compounding
A 1% annual fee sounds small. Over 30 years, it's devastating:
| 0% Fee | 1% Fee | 2% Fee | |
|---|---|---|---|
| $10K at 8% for 30 years | $109,357 | $76,123 | $57,435 |
| Amount lost to fees | $0 | $33,234 | $51,922 |
| % of returns consumed | 0% | 30.4% | 47.5% |
A 1% fee consumes 30% of your total returns over 30 years. A 2% fee takes nearly half. This is why low-cost index funds (VFIAX at 0.04%, VTSAX at 0.04%) have crushed actively managed funds (typically 1-2%) over long periods. The fee difference alone can be worth hundreds of thousands of dollars.
Key Takeaways
- Compound interest = earning returns on returns — exponential growth, not linear
- A = P(1 + r/n)^(nt) — n=12 for monthly compounding, n=365 for daily
- Rule of 72: 72 ÷ rate = years to double. At 10%, money doubles every 7.2 years
- Starting 10 years earlier beats investing 3× more money — time > amount
- A 1% fee consumes 30% of your returns over 30 years — use low-cost index funds