How Compound Interest Works
The compound interest formula
Compound interest is calculated using the formula:
This tells you the final amount A after applying interest that compounds over time.
What each variable means
| Variable | Meaning | Example |
|---|---|---|
| A | Final amount (principal + interest) | $16,288.95 |
| P | Principal — your starting amount | $10,000 |
| r | Annual interest rate as a decimal | 0.05 (= 5%) |
| n | Number of times interest compounds per year | 12 (monthly) |
| t | Time in years | 10 |
Using those example values: $10,000 at 5% compounded monthly for 10 years gives $10,000 × (1 + 0.05/12)^(12×10) = $16,470.09.
Why compounding frequency matters
The more frequently interest compounds, the more you earn — because each period’s interest gets added to the base before the next period’s interest is calculated.
Here’s a concrete example: $10,000 at 10% per year for 10 years, with different compounding frequencies.
| Frequency | n (per year) | Final Amount | Interest Earned |
|---|---|---|---|
| Annually | 1 | $25,937.42 | $15,937.42 |
| Semi-annually | 2 | $26,532.98 | $16,532.98 |
| Quarterly | 4 | $26,850.64 | $16,850.64 |
| Monthly | 12 | $27,070.41 | $17,070.41 |
| Daily | 365 | $27,179.10 | $17,179.10 |
Going from annual to monthly compounding adds over $1,100 on a $10,000 investment over 10 years — with no extra contribution required.
The Rule of 72
The Rule of 72 is a quick mental shortcut to estimate how long it takes to double your money at a fixed annual rate:
| Annual Rate | Rule of 72 estimate | Exact years |
|---|---|---|
| 2% | 36 years | 35.0 years |
| 4% | 18 years | 17.7 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
| 12% | 6 years | 6.1 years |
The Rule of 72 is surprisingly accurate between 6%–12% and is a useful sanity check against any investment claim.
Simple interest vs compound interest
Simple interest only applies to the original principal — it never grows on itself. Compound interest adds earned interest back to the principal each period, so future interest is calculated on a larger base.
$10,000 at 7% for 20 years:
Compound interest more than doubled the interest earned compared to simple interest over 20 years. This is the core reason long-term investing is so powerful — time amplifies the compounding effect.
When each type applies in real life
- Simple interest — short-term loans, car loans, some bonds, and treasury bills
- Compound interest (investments) — savings accounts, index funds, retirement accounts (401k, IRA), and most long-term wealth building
- Compound interest (debt) — credit cards, student loans, and mortgages — compounding works against you here, so paying down debt early saves significantly