What Is Compound Interest?
Compound interest is often called the "eighth wonder of the world" — and for good reason. Unlike simple interest, which is calculated only on your original principal, compound interest is calculated on both your principal and the interest you've already earned. Over time, this creates a snowball effect that can dramatically grow your savings or, if you're in debt, dramatically increase what you owe.
Simple vs. Compound Interest: A Quick Comparison
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Calculated on | Principal only | Principal + accrued interest |
| Growth over time | Linear | Exponential |
| Better for savers? | No | Yes |
| Better for borrowers? | Yes | No |
The Formula Behind Compound Interest
The compound interest formula is:
A = P(1 + r/n)nt
- A — the final amount (principal + interest)
- P — the principal (your starting amount)
- r — annual interest rate (as a decimal, e.g. 5% = 0.05)
- n — number of times interest compounds per year
- t — time in years
A Real-World Example
Let's say you invest $5,000 at a 6% annual interest rate, compounded monthly, for 20 years.
Plugging into the formula: A = 5000 × (1 + 0.06/12)12×20
Result: approximately $16,551. Your money more than tripled — and you didn't contribute a single extra dollar.
How Compounding Frequency Matters
The more frequently interest compounds, the more you earn. Here's how different compounding schedules affect a $10,000 investment at 5% over 10 years:
- Annually: ~$16,289
- Quarterly: ~$16,436
- Monthly: ~$16,470
- Daily: ~$16,487
While the differences seem small at first, they become significant with larger principals and longer time horizons.
The Rule of 72: A Mental Math Shortcut
Want to quickly estimate how long it takes to double your money? Use the Rule of 72: divide 72 by your annual interest rate.
Example: At 6% interest, your money doubles in approximately 72 ÷ 6 = 12 years.
The Dark Side: Compound Interest on Debt
Compound interest works against you when you're the borrower. Credit card debt, for instance, often compounds daily. If you carry a balance, interest accrues on top of interest — which is why balances can spiral quickly.
Key takeaway: Pay off high-interest debt as aggressively as you invest. The same math that builds wealth can destroy it.
Takeaways
- Start investing early — time is the most powerful variable in the compound interest formula.
- Reinvest your earnings rather than withdrawing interest.
- Compare compounding frequencies when choosing savings accounts.
- Treat high-interest debt as a financial emergency.