How Compound Interest Works
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Albert Einstein reportedly called it "the eighth wonder of the world" — and with good reason. The longer money compounds, the more dramatically it grows.
The difference between simple and compound interest becomes striking over long periods. $10,000 invested at 7% simple interest for 30 years grows to $31,000. With monthly compounding, that same $10,000 grows to over $81,000 — nearly 3× more, from the same initial investment.
The Compound Interest Formula
The standard compound interest formula is:
| Variable | Meaning |
|---|---|
| A | Final amount (future value) |
| P | Principal (initial investment) |
| r | Annual interest rate (as decimal) |
| n | Compounding frequency per year |
| t | Time in years |
Example: $10,000 at 7% Over 30 Years
| Compounding | Future Value | Interest Earned |
|---|---|---|
| Annual | $76,122 | $66,122 |
| Monthly | $81,165 | $71,165 |
| Daily | $81,635 | $71,635 |
More frequent compounding produces marginally higher returns. The difference between monthly and daily compounding is small, but the difference between annual and daily is meaningful over decades.
The Power of Regular Contributions
Adding even modest monthly contributions dramatically accelerates growth. Adding $200/month to that same $10,000 at 7% over 30 years grows to over $281,000 — compared to $81,000 without contributions. Regular contributions add $72,000 in contributions but generate over $129,000 in additional interest.
Rule of 72
A quick mental shortcut: divide 72 by your interest rate to estimate how many years until your money doubles. At 7%, money doubles roughly every 72 ÷ 7 = 10.3 years. At 10%, it doubles every 7.2 years.