Compound interest is often called the most powerful force in personal finance. It's the reason why someone who starts investing at 25 can retire with more money than someone who invests twice as much but starts at 35. Understanding how it works is essential for anyone who wants to build wealth.
Simple vs. Compound Interest
With simple interest, you earn interest only on your original investment (the principal). With compound interest, you earn interest on your principal plus all the interest you've already earned. This creates exponential growth instead of linear growth.
Simple interest: $10,000 + ($700 × 20) = $24,000
Compound interest: $10,000 × (1.07)²⁰ = $38,697
The difference: $14,697 — that's free money from compounding.
The Formula
A = final amount · P = principal · r = annual rate
n = compounds per year · t = years
For most practical purposes, you can simplify: if interest compounds annually, the formula is just A = P × (1 + r)^t. The more frequently interest compounds (monthly, daily), the slightly more you earn — but the difference between monthly and daily compounding is minimal.
The Rule of 72
Want to know how long it takes to double your money? Divide 72 by the interest rate. This approximation is remarkably accurate for rates between 4% and 15%.
| Rate | Doubling Time |
|---|---|
| 4% | ~18 years |
| 6% | ~12 years |
| 8% | ~9 years |
| 10% | ~7.2 years |
| 12% | ~6 years |
The Power of Starting Early
This is the most important concept in compound interest. Time is the multiplier that makes everything work.
Alice starts at 25, stops at 65 (40 years):
Total invested: $96,000
Final balance: ~$525,000
Bob starts at 35, stops at 65 (30 years):
Total invested: $72,000
Final balance: ~$243,000
Alice invested only $24,000 more but ended up with $282,000 more. That's the 10-year head start compounding.
Compounding Frequency
Interest can compound annually, quarterly, monthly, or daily. More frequent compounding means slightly more earnings, but the differences are smaller than most people think. $10,000 at 7% for 20 years: annually = $38,697, monthly = $40,387, daily = $40,552. The jump from annual to monthly matters; monthly to daily barely does.
Real-World Considerations
These calculations show nominal returns before inflation and taxes. With average inflation of 2-3%, a 7% nominal return is roughly a 4-5% real return. Tax-advantaged accounts (401k, IRA, ISA) let your money compound without annual tax drag, which significantly improves long-term growth. Investment returns also aren't constant — the stock market fluctuates year to year. Historical average returns for a diversified stock portfolio have been roughly 7-10% annually over long periods, but individual years can vary dramatically.