Compound Interest Explained
Interest that earns interest. It's how small savings become large ones over time, and how credit card debt spirals. See it happen with your own numbers.
Simple vs compound interest
Simple interest is paid only on the money you put in. Compound interest is also paid on the interest you've already earned, so it snowballs.
| Year | Simple 10% on $1,000 | Compound 10% on $1,000 |
|---|---|---|
| 0 | $1,000 | $1,000 |
| 1 | $1,100 | $1,100 |
| 2 | $1,200 | $1,210 |
| 5 | $1,500 | $1,611 |
| 10 | $2,000 | $2,594 |
| 20 | $3,000 | $6,727 |
For the first couple of years they look almost the same. Then compound pulls away dramatically.
The formula
- r = 0.05, n = 12, t = 10
- 1 + 0.05/12 = 1.0041667
- 1.0041667120 ≈ 1.647
- 5,000 × 1.647
- ≈ $8,235
More frequent compounding helps a little, but time and the rate matter far more.
The rule of 72
A quick way to estimate how long it takes money to double:
| Rate | Doubles in about |
|---|---|
| 2% | 36 years |
| 4% | 18 years |
| 6% | 12 years |
| 8% | 9 years |
| 24% (credit card) | 3 years |
Start early. At 6%, $1,000 doubles roughly every 12 years. Invested at 25, it's about $16,000 by 73. Wait until 37 and it's only $8,000: one fewer doubling.
Compounding works against you on debt
Credit cards compound too, often at 20–30% a year. An unpaid $2,000 balance at 24% grows to about $2,540 in one year if you pay nothing, and roughly doubles in three.
Minimum payments trap: paying only the minimum mostly covers interest, so the balance barely shrinks. Paying off high-interest debt is like earning a guaranteed 20%+ return.
Assumes monthly compounding and a steady rate. Real investments go up and down, and this isn't financial advice.