Compound interest: real numbers
Key takeaways
04 · ideas- Starting at 25 vs 35 creates a $400k+ gap at 65
- $10,000 invested at 7% for 30 years = $76,123
- The last decade of a 30-year investment generates more than the first 20 years
- Time is the most powerful investment variable — more than rate or amount
Basic level
The essentials · 1 min
Compound interest means your returns generate their own returns. A $10,000 investment at 7% earns $700 in year 1. In year 2, you earn 7% on $10,700 — not just the original $10,000. Over decades, this creates exponential rather than linear growth.
The Rule of 72: Divide 72 by your annual return to find how long it takes to double your money.- 7% return → doubles every ~10.3 years
- 10% return → doubles every ~7.2 years
- Starting at 25 → $1,315,000 at age 65
- Starting at 35 → $608,000 at age 65
- Difference: $707,000 — from just 10 extra years of contributions
The first 10 years generated more than the last 30 years combined, because money invested early has the most time to compound.
Intermediate level
How it applies · 2 min
The compounding table
$10,000 invested once, never touched:
| Years | At 5% | At 7% | At 10% |
|---|---|---|---|
| 10 | $16,289 | $19,672 | $25,937 |
| 20 | $26,533 | $38,697 | $67,275 |
| 30 | $43,219 | $76,123 | $174,494 |
| 40 | $70,400 | $149,745 | $452,593 |
Notice: at 10%, the amount more than doubles every 7 years. At 30 years it's $174,494; at 40 years, $452,593 — the last decade alone adds $278,000 to a single $10,000 investment.
Monthly contributions vs. lump sum
Most people build wealth through regular monthly contributions, not lump sums.
$500/month at 7% for different starting ages (retiring at 65):
| Start age | Years invested | Total contributed | Portfolio at 65 |
|---|---|---|---|
| 22 | 43 | $258,000 | $1,800,000 |
| 25 | 40 | $240,000 | $1,315,000 |
| 30 | 35 | $210,000 | $900,000 |
| 35 | 30 | $180,000 | $608,000 |
| 40 | 25 | $150,000 | $398,000 |
| 45 | 20 | $120,000 | $248,000 |
The difference between starting at 22 vs 35 is $1.2M — with only $78,000 more contributed. The extra money came from 13 extra years of compounding.
The inflation-adjusted perspective
At 7% nominal with 3% inflation, real return is ~3.9%. A $1,315,000 portfolio at 65 sounds impressive, but in today's dollars at 3% inflation over 40 years, it's worth ~$404,000. Still excellent — but understanding real returns matters for retirement planning.
Advanced level
The math, step by step · 2 min
The mathematics of compound growth
For a single lump sum P at rate r for t years:The time value of early years: The contribution to final value from year k of a stream of contributions is proportional to (1+r_m)^{n-12k}. Contributions in year 1 grow for the full n months; contributions in year t grow for only n - 12t months.
Sensitivity to rate: The partial derivative of FV with respect to r:For P = \10,000, t = 30: a 1% increase in rate increases final value by approximately \$10,000 \times 30 \times (1.07)^{29} \approx \$135,000$. This explains why expense ratios and rate differences compound dramatically over long time horizons.
The Einstein attribution to compound interest as the "8th wonder" is likely apocryphal — but the math supports the sentiment. At 7%, a dollar doubles every 10 years. At age 20, you have four doublings until 60: $1 → $2 → $4 → $8 → $16. At age 40, you have only two doublings: $1 → $2 → $4. The 20-year-old's dollar grows 4x more — purely from time.