The short version
Compound interest is interest earned on interest. Each period, the interest is added to your balance, and the next period's interest is calculated on that larger balance. Over short periods the effect is small. Over decades it becomes the main source of growth.
It also works in reverse. On a credit card or loan, unpaid interest is added to what you owe, and you then pay interest on that interest.
A simple example
Suppose you save 1,000 at 8% a year, and the interest is added once a year.
| Year | Starting balance | Interest (8%) | Ending balance |
|---|---|---|---|
| 1 | 1,000.00 | 80.00 | 1,080.00 |
| 2 | 1,080.00 | 86.40 | 1,166.40 |
| 3 | 1,166.40 | 93.31 | 1,259.71 |
| 10 | 1,999.00 | 159.92 | 2,158.92 |
| 20 | 4,315.70 | 345.26 | 4,660.96 |
| 30 | 9,317.27 | 745.38 | 10,062.66 |
The interest in year 1 is 80. By year 30 it is about 745 in a single year, without you adding anything. That acceleration is compounding. The figures work the same in any currency.
The formula in plain English
The standard formula is:
A = P × (1 + r/n)^(n × t)
- A is the final amount.
- P is the principal, the amount you start with.
- r is the annual interest rate as a decimal (8% = 0.08).
- n is how many times a year interest is added (1 for yearly, 12 for monthly).
- t is the number of years.
For 1,000 at 8% compounded monthly for 10 years: 1,000 × (1 + 0.08/12)^(120) ≈ 2,219.64. Compounded yearly, it is 2,158.92. More frequent compounding helps a little, but the rate and the time matter far more.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual interest rate.
- At 6%, money doubles in about 72 ÷ 6 = 12 years.
- At 8%, about 9 years.
- At 12%, about 6 years.
It works for debt too. A credit card balance at 24% doubles in about 3 years if nothing is paid.
Why starting early matters so much
Compare two savers who each earn 7% a year:
- Aisha saves 200 a month from age 25 to 35, then stops. She contributes 24,000 in total.
- Bilal saves 200 a month from age 35 to 65. He contributes 72,000 in total.
At 65, Aisha ends up with a larger balance than Bilal despite contributing a third as much, because her money had an extra ten years to compound before Bilal started. The exact figures depend on the return, but the lesson holds: time is the most powerful ingredient, and the cost of waiting is high.
Making compounding work for you
- Start as early as you can, even with small amounts.
- Reinvest the returns. Interest or dividends that you spend cannot compound.
- Keep fees low. A 1–2% annual fee compounds too, and over decades it can take a large share of your returns.
- Be consistent. Regular automatic contributions matter more than perfect timing.
- Account for inflation. What matters is the return above inflation. Money earning 5% while prices rise 6% is losing buying power.
For a step-by-step start, see our beginner's guide to investing.
When compounding works against you
High-interest debt compounds just as reliably as savings:
- Credit cards often charge high annual rates and can compound daily, so a balance you only pay the minimum on can last for years.
- Payday and informal loans can carry extremely high effective rates.
- Buy-now-pay-later plans can become expensive once late fees and interest apply.
Paying off high-interest debt is usually the best guaranteed "return" available. Clearing a card charging 24% is like earning 24% risk-free. A clear budget helps you find the money to do it.
Key takeaways
- Compound interest is interest on interest, and it accelerates over time.
- The rate and, above all, the number of years matter most.
- Use the Rule of 72 for quick doubling estimates.
- Start early, reinvest, keep fees low, and pay down high-interest debt first.