What Is Compound Interest?
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In simple terms: you earn interest on your interest.
This is different from simple interest, which only applies to the original principal.
The Formula
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 = number of years
Try It Yourself
See how your money could grow with our compound interest calculator:
Simple Interest vs. Compound Interest
Let's compare $10,000 invested at 7% annual interest over 30 years:
| Year | Simple Interest | Compound Interest | Difference |
|---|---|---|---|
| 1 | $10,700 | $10,700 | $0 |
| 5 | $13,500 | $14,026 | $526 |
| 10 | $17,000 | $19,672 | $2,672 |
| 20 | $24,000 | $38,697 | $14,697 |
| 30 | $31,000 | $76,123 | $45,123 |
After 30 years, compound interest produces more than double what simple interest does. That's the power of exponential growth.
The Rule of 72
Want a quick way to estimate how long it takes to double your money? Divide 72 by your interest rate:
Years to double = 72 ÷ interest rate
Examples:
- At 6% → 72 ÷ 6 = 12 years
- At 8% → 72 ÷ 8 = 9 years
- At 10% → 72 ÷ 10 = 7.2 years
- At 12% → 72 ÷ 12 = 6 years
How Compounding Frequency Matters
The more frequently interest compounds, the more you earn. Here's $10,000 at 8% annual rate over 10 years:
| Compounding | Final Amount | Interest Earned |
|---|---|---|
| Annually | $21,589 | $11,589 |
| Quarterly | $21,911 | $11,911 |
| Monthly | $22,196 | $12,196 |
| Daily | $22,253 | $12,253 |
The difference between annual and daily compounding is $664 — not huge, but it adds up over longer time periods and larger amounts.
Why Starting Early Matters More Than Starting Big
Consider two investors:
Alice starts investing $200/month at age 25, stops at 35 (10 years, $24,000 total invested).
Bob starts investing $200/month at age 35, continues until 65 (30 years, $72,000 total invested).
Assuming 8% annual returns:
- Alice at 65: $314,870 (from $24,000 invested)
- Bob at 65: $298,072 (from $72,000 invested)
Alice invested one-third as much money but ended up with more — because compound interest had 10 extra years to work.
Where to Find Compound Interest
Compound interest works in many financial products:
It Works FOR You
- Savings accounts — typically compound daily or monthly
- CDs (Certificates of Deposit) — fixed rate with guaranteed compounding
- Index funds and ETFs — reinvested dividends compound over time
- Bonds — reinvested coupon payments
It Works AGAINST You
- Credit card debt — compounds daily at 15-25% APR
- Student loans — interest capitalizes if unpaid
- Mortgages — most of early payments go to interest
The key insight: make compound interest your ally by investing early and avoiding high-interest debt.
Key Takeaways
- Compound interest means earning interest on interest — it grows exponentially
- The Rule of 72 gives a quick estimate for doubling time
- More frequent compounding = slightly more growth
- Starting early matters more than investing more money later
- Compound interest works both for (investments) and against you (debt)
- Even small regular contributions can grow into significant amounts over decades