Compound interest is often called the 8th wonder of the world. Unlike simple interest, it applies not only to your initial capital but also to the interest already earned.
Simple vs Compound Interest
Simple Interest
With $10,000 at 5% per year for 10 years:
- Annual interest: $500 every year
- Total after 10 years: $15,000
Compound Interest
With the same conditions, interest is added to the principal:
| Year | Starting Balance | Interest | Ending Balance |
|---|---|---|---|
| 1 | $10,000 | $500 | $10,500 |
| 2 | $10,500 | $525 | $11,025 |
| 5 | $12,763 | $638 | $13,401 |
| 10 | $15,513 | $776 | $16,289 |
Result after 10 years: $16,289 ($1,289 more than simple interest)
The Compound Interest Formula
A = P × (1 + r/n)^(n × t)
- A = final amount
- P = initial principal
- r = annual interest rate (decimal)
- n = number of times interest is compounded per year
- t = time in years
The Rule of 72
A simple rule to estimate how long it takes to double an investment:
Years to double = 72 ÷ annual interest rate
Examples:
- At 4% → 72 ÷ 4 = 18 years
- At 6% → 72 ÷ 6 = 12 years
- At 9% → 72 ÷ 9 = 8 years
Compounding Frequency
The more often interest is compounded, the higher the final amount:
| Frequency | $10,000 at 6% for 10 years |
|---|---|
| Annually | $17,908 |
| Semi-annually | $18,061 |
| Monthly | $18,194 |
| Daily | $18,221 |
Starting Early: The Power of Time
Time is the most powerful factor in compound interest.
Example: Sarah starts saving $200/month at age 25. John starts at 35. At age 65, with a 7% return:
- Sarah: $525,000 (invested $96,000 total)
- John: $243,000 (invested $72,000 total)
Sarah invested only $24,000 more but ends up with $282,000 extra thanks to 10 additional years of compounding.
Pitfalls to Watch Out For
Compound Interest Works Against You Too
High-interest debt (credit cards, payday loans) works on the same principle. A 20% annual credit card rate doubles your debt in less than 4 years.
Inflation
A 5% return with 3% inflation only enriches you by 2% in real terms per year. Always think in terms of real returns.
Conclusion
Compound interest is your best ally for building long-term wealth. The key: start early, be consistent, and let time do the work.