Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal, compound interest causes your money to grow at an accelerating rate - often called “exponential growth.”
Simple vs. Compound Interest
With simple interest, if you invest $10,000 at 7% per year for 10 years, you earn $700 each year for a total of $7,000 in interest.
With compound interest at the same rate, your $10,000 grows to over $19,600 - nearly double what simple interest produces. That extra $2,600 comes purely from earning interest on your interest.
The Formula
The compound interest formula is:
A = P(1 + r/n)^(nt)
Where:
- 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 mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money.
- At 6% → money doubles in ~12 years
- At 8% → money doubles in ~9 years
- At 12% → money doubles in ~6 years
Compounding Frequency Matters
The more frequently interest compounds, the more you earn:
| Frequency | $10,000 at 7% after 20 years |
|---|---|
| Annually | $38,697 |
| Quarterly | $39,515 |
| Monthly | $39,794 |
| Daily | $39,857 |
Starting Early is Everything
The most powerful variable is time. Starting 10 years earlier can result in twice as much wealth at retirement, even with the same contributions.
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