Compound Interest, Explained
Compound interest means earning returns on your returns — interest calculated not just on your original deposit, but on all the interest it has already earned. It's the reason time matters more than timing in investing.
Key takeaways
- Compound interest = earning returns on your returns: A = P(1 + r/n)nt.
- Starting early beats investing more: $5,000/yr for 10 years from age 25 grows to about $602,000 by 65 at 7% — more than $5,000/yr for 30 years starting at 35 ($540,000).
- The Rule of 72: divide 72 by the annual return to estimate doubling time (about 9 years at 8%).
- Compounding works against you too: unpaid debt grows exponentially the same way.
The formula
A = final amount · P = principal · r = annual rate (as a decimal) · n = compounding periods per year · t = years
Each period, the balance is multiplied by (1 + r/n). Because the base keeps growing, the dollar gains accelerate — growth is exponential, not linear.
Why starting early beats investing more
Compare two investors earning 7% annually:
| Investor | Invests | Total contributed | Value at 65 |
|---|---|---|---|
| Early, age 25–35 | $5,000/yr for 10 yrs | $50,000 | $602,000 |
| Late, age 35–65 | $5,000/yr for 30 yrs | $150,000 | $540,000 |
The early investor contributed one-third as much and still ended up ahead. The extra 10 years of compounding did more work than 20 extra years of contributions. This is the single most important intuition in personal finance.
Does compounding frequency matter?
On $10,000 at 7% for 20 years:
| Compounds | Final value |
|---|---|
| Annually | $38,697 |
| Monthly | $40,387 |
| Daily | $40,548 |
Daily beats annual by about 5% — nice, but dwarfed by the effect of an extra few years or a slightly higher rate. Don't chase compounding frequency; chase time in the market and low fees.
The Rule of 72
A quick mental shortcut: divide 72 by your annual return to estimate doubling time. At 7%, money doubles roughly every 10 years (72 ÷ 7 ≈ 10.3). At 10%, every ~7 years. Accurate enough for rates between about 4% and 12%.
Compounding works against you, too
Credit card debt at 24% APR compounds the same way — in reverse. A $5,000 balance making minimum payments can take over a decade to clear and cost nearly as much in interest as the original debt. The math doesn't care which direction it's pointed.
See your own growth curve
Enter your balance, monthly contributions, and expected return to project the compounding year by year.
Open the Compound Interest CalculatorFrequently asked questions
What is compound interest in simple terms?
Earning interest on your interest. Each period your balance grows, and the next period's interest is calculated on the bigger balance.
What's the compound interest formula?
A = P(1 + r/n)nt — final amount equals principal times one plus the per-period rate, raised to the number of periods.
How often should interest compound?
More frequent is slightly better, but the difference between monthly and daily is small. Time and rate dominate.
What is the Rule of 72?
72 ÷ annual return ≈ years to double your money. At 8%, about 9 years.
Can I lose money with compound interest?
Compounding amplifies whatever the return is — including negative years in the market. Over long periods, diversified market returns have historically been positive, but there are no guarantees.
Educational content, not financial advice. Investment returns vary and past performance doesn't guarantee future results.