Compound interest is often called the "eighth wonder of the world" — a quote frequently attributed to Albert Einstein. Whether or not Einstein actually said it, the principle behind compound interest truly is remarkable and forms the foundation of wealth building.
Simple Definition
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In simple terms, it's "interest on interest."
Key Takeaway
With compound interest, your money earns money, and then that money earns even more money. This creates exponential growth over time.
Compound Interest vs Simple Interest
The difference between simple and compound interest might seem small at first, but over time it becomes dramatic:
- Simple Interest: Interest is calculated only on the original principal. If you invest $1,000 at 5% simple interest, you earn $50 every year, regardless of how much has accumulated.
- Compound Interest: Interest is calculated on the principal plus all accumulated interest. Your $1,000 earns $50 in year one, but in year two you earn interest on $1,050, giving you $52.50.
The Compound Interest Formula
The mathematical formula for compound interest is:
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 = Number of years
Real-World Example
Let's say you invest $10,000 at 7% annual return (a typical stock market average):
| Years | Simple Interest | Compound Interest | Difference |
|---|---|---|---|
| 10 | $17,000 | $19,672 | +$2,672 |
| 20 | $24,000 | $38,697 | +$14,697 |
| 30 | $31,000 | $76,123 | +$45,123 |
| 40 | $38,000 | $149,745 | +$111,745 |
After 40 years, compound interest has earned you nearly 4 times more than simple interest would have!
Why Time is Your Greatest Asset
The most powerful factor in compound interest isn't the interest rate or the amount you invest — it's time. The longer your money compounds, the more dramatic the growth becomes.
This is why financial advisors always emphasize starting early. Someone who invests $200/month starting at age 25 will likely have more at retirement than someone who invests $400/month starting at age 35.
Try It Yourself
The best way to understand compound interest is to see it in action. Use our free calculator to visualize how your investments could grow over time.
See Compound Interest in Action
Try our free compound interest calculator to visualize how your money grows over time with beautiful interactive charts.
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