Compound Interest Explained: How Your Money Grows Exponentially
Learn how compound interest works, see the math behind exponential growth, and calculate how much your investments will grow over time.
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Albert Einstein allegedly called compound interest "the eighth wonder of the world." Whether or not he actually said it, the principle is undeniably powerful: compound interest earns interest on your interest, creating exponential growth that accelerates over time.
Simple Interest vs. Compound Interest
With simple interest, you earn interest only on your original principal. With compound interest, each interest payment is added to your principal, and future interest is calculated on the larger amount.
| Year | Simple Interest (5% on $10,000) | Compound Interest (5% on $10,000) |
|---|---|---|
| 1 | $10,500 | $10,500 |
| 5 | $12,500 | $12,763 |
| 10 | $15,000 | $16,289 |
| 20 | $20,000 | $26,533 |
| 30 | $25,000 | $43,219 |
After 30 years, compound interest produces 73% more than simple interest on the same principal.
The Compound Interest 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 = number of years
Compounding Frequency Matters
The more frequently interest compounds, the faster your money grows:
| Frequency | $10,000 at 5% After 10 Years |
|---|---|
| Annually (n=1) | $16,289 |
| Quarterly (n=4) | $16,436 |
| Monthly (n=12) | $16,470 |
| Daily (n=365) | $16,487 |
The difference between annual and daily compounding is relatively small. The much bigger factor is time — the longer you let compound interest work, the more dramatic the results.
The Rule of 72
Want to know how long it takes to double your money? Divide 72 by the interest rate. At 6% annual returns, your money doubles in approximately 72/6 = 12 years. At 8%, it doubles in 9 years. At 10%, just 7.2 years.
The Power of Starting Early
Consider two investors:
- Alice invests $200/month from age 25 to 35 (10 years), then stops. Total invested: $24,000.
- Bob invests $200/month from age 35 to 65 (30 years). Total invested: $72,000.
Assuming 7% annual returns, Alice ends up with more money at age 65 than Bob, despite investing only one-third as much. This is the power of compound interest over time.
Where Compound Interest Works Against You
Compound interest also applies to debt. Credit card interest compounds on your unpaid balance, which is why a $5,000 credit card balance at 22% APR can take decades to pay off with minimum payments — and cost you more in interest than the original balance. Always pay more than the minimum.
Try our compound interest calculator to see exactly how your money could grow with different rates, time periods, and monthly contributions.