Compound Interest Explained: How Your Money Grows Faster Than You Think
Compound interest is often called the eighth wonder of the world. Here's the math behind it, the Rule of 72 shortcut, and why starting early matters more than starting big.
Albert Einstein is often (probably apocryphally) credited with calling compound interest "the eighth wonder of the world." Whether or not he actually said it, the underlying idea is one of the most powerful forces in personal finance — and one of the most misunderstood.
Simple Interest vs. Compound Interest
Simple interest is calculated only on your original principal. If you invest $10,000 at 7% simple interest, you earn $700 every year, forever — a flat, linear line.
Compound interest is calculated on your principal **plus** all the interest you've already earned. That $700 in year one becomes part of your balance, so in year two you earn interest on $10,700, not just $10,000. Over time, this creates exponential rather than linear growth.
The Rule of 72
Want a quick mental shortcut for how long it takes an investment to double? Divide 72 by your annual rate of return:
- At 6%: 72 / 6 = 12 years to double
- At 8%: 72 / 8 = 9 years to double
- At 10%: 72 / 10 = 7.2 years to double
It's not perfectly precise, but it's remarkably close for typical long-term rates of return.
Why Starting Early Beats Starting Big
Here's the part that surprises most people: an investor who starts 10 years earlier with smaller monthly contributions often ends up **ahead** of someone who starts later with much larger contributions, purely because of the extra time compounding has to work.
Consider two people investing at 7% annually: - **Investor A** starts at age 25, contributes $300/month until age 65 (40 years) - **Investor B** starts at age 35, contributes $500/month until age 65 (30 years)
Investor A contributes less money in total ($144,000 vs. $180,000) but ends up with a noticeably larger final balance, because those first 10 years of compounding are irreplaceable.
Worked Example
Investing $10,000 upfront with $300/month contributions at a 7% annual return for 20 years:
- Total contributed: $10,000 + ($300 × 240 months) = $82,000
- Projected final balance: ≈ $170,000
- Interest earned: ≈ $88,000 — more than everything you put in
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See how your investments grow over time with compound interest. Compare different rates, add monthly contributions, and visualize the power of compounding.