Compound Interest
"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it."- Attributed to Albert Einstein
The Formula
A = P(1 + r/n)^(nt)
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate (decimal)
- n = Number of times interest compounds per year
- t = Time in years
The Rule of 72
A quick way to estimate how long it will take to double your money:
Years to double = 72 ÷ Annual interest rate (%)
- At 6% interest, money doubles in ~12 years
- At 8% interest, money doubles in ~9 years
- At 10% interest, money doubles in ~7.2 years
Example: $10,000 at 7% for 30 Years
| Year | Value | Interest Earned |
|---|---|---|
| 0 | $10,000 | $0 |
| 10 | $19,672 | $9,672 |
| 20 | $38,697 | $28,697 |
| 30 | $76,123 | $66,123 |
Note: This example assumes annual compounding. More frequent compounding would result in slightly higher returns.
The Power of Time
The true power of compound interest becomes apparent over long time periods. Consider two investors:
| Investor | Strategy | Total Invested | Final Value at 65 |
|---|---|---|---|
| Early Emma | $5,000/year from age 25-35 (10 years), then stops | $50,000 | $602,070 |
| Late Larry | $5,000/year from age 35-65 (30 years) | $150,000 | $540,741 |
Assumes 8% annual return. Despite investing 3x less money, Early Emma ends up with more due to the extra years of compounding.
Key Insights
- Time is your greatest ally: The longer your money compounds, the more dramatic the growth. The final years of a long compounding period produce the most significant gains.
- Start early: Even small amounts invested early can outperform larger amounts invested later. A 10-year head start can make a massive difference in final outcomes.
- Reinvest returns: To fully harness compound interest, reinvest dividends and interest payments rather than spending them.
- Avoid withdrawals: Taking money out disrupts the compounding process and significantly reduces long-term growth. Each withdrawal costs you not just the amount withdrawn but all future returns on that amount.
- Small rate increases matter: Even a 1-2% increase in your rate of return can lead to dramatically different outcomes over long periods.
Real-World Applications
- Retirement accounts: 401(k)s, IRAs, and other retirement vehicles are designed to take advantage of compound growth over decades.
- Index fund investing: Low-cost index funds allow you to capture market returns and reinvest dividends automatically.
- Debt (the dark side): Compound interest works against you with credit card debt and other high-interest loans. A 20% credit card interest rate compounds just as powerfully as a 20% investment return, but in the wrong direction.
- Dollar-cost averaging: Regular, consistent investing allows you to maximize the time your money has to compound.