Money guide
Compound vs simple interest and the Rule of 72
Simple interest grows by the same amount every year. Compound interest grows by the same percentage every year, so each year's growth is bigger than the last. Over long periods the difference is dramatic.
Simple interest
Simple interest is only ever paid on the original amount.
Interest = principal × rate × years
$5,000 at 6% for 10 years: $5,000 × 0.06 × 10 = $3,000 → $8,000 total
Compound interest
With compounding, interest is added to the balance and then earns interest itself.
Final amount = principal × (1 + rate)^years
$5,000 at 6% for 10 years: $5,000 × 1.06^10 = $5,000 × 1.7908 = $8,954.24
| Years | Simple interest | Compound interest | Difference |
|---|---|---|---|
| 10 | $8,000.00 | $8,954.24 | $954.24 |
| 30 | $14,000.00 | $28,717.46 | $14,717.46 |
After 30 years, compounding has more than doubled the simple-interest result. This is why starting early matters more than almost anything else for long-term saving.
How often interest compounds
Interest can be added yearly, monthly, or daily. More frequent compounding gives slightly more growth, which is why savings accounts often quote an APY (annual percentage yield) alongside the rate.
APY = (1 + rate ÷ n)^n − 1, where n = times per year
6% compounded monthly: (1 + 0.005)^12 − 1 ≈ 6.17% APY
$5,000 for 10 years monthly: $5,000 × 1.005^120 ≈ $9,096.98
The Rule of 72
To estimate how many years it takes money to double, divide 72 by the yearly percentage rate. It is a mental shortcut, and it is surprisingly accurate for everyday rates.
Years to double ≈ 72 ÷ rate
At 6%: 72 ÷ 6 = about 12 years
Working backwards, to double in 8 years you need about 72 ÷ 8 = 9% a year.
| Yearly rate | Rule of 72 | Exact years |
|---|---|---|
| 2% | 36 | 35.0 |
| 4% | 18 | 17.7 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6 | 6.1 |
It works for debt and inflation too
The same rule tells you how fast a debt doubles if left unpaid: at 24% interest, about every 3 years. It also shows how quickly prices double: at 3% inflation, roughly every 24 years. See the credit card APR guide and the inflation guide for worked examples.
Real investments rarely grow at a steady rate. The investment returns and compounding guide explains why losses and uneven years change the picture. Returns are never guaranteed, and this guide is general education, not investment advice.