Money guide · Investing basics, fees, and risk
Compound interest explained: formula and examples
Calculate compound growth and distinguish a constant-rate illustration from a forecast of investment returns.
How it works
Interest retained in an account can earn interest in later periods. Investment gains can also compound, but market returns fluctuate and losses compound too. The formula needs a rate matching the period: monthly periods require a corresponding monthly rate. Contributions and withdrawals need a cash-flow calculation rather than only the initial-principal formula.
A worked example
At a hypothetical constant 5% annual rate, $1,000 becomes $1,050 after one year and $1,102.50 after two. After ten years it is $1,000 × 1.05^10, approximately $1,628.89. The $628.89 gain exceeds the $500 from ten years of simple interest at the same initial principal. This excludes taxes, fees, and additional deposits.
What to compare
State the compounding interval, whether the rate is an interest rate or APY, and when cash flows occur. Subtract appropriate costs and evaluate inflation separately. A 5% nominal annual gain with 3% inflation corresponds to about 1.94% real growth: 1.05 / 1.03 − 1. Avoid subtracting inflation twice from already adjusted figures.
A common mistake to avoid
A fixed-rate example is not evidence that an investment will earn that rate each year. Do not plug an average market return into the formula and treat the result as a promise. Timing, volatility, taxes, and costs can produce materially different outcomes, particularly when withdrawals are involved.
Is APY the same as the stated interest rate?
Not always. APY includes compounding under its assumptions, while a stated interest rate may use a particular compounding schedule.
Sources and further reading
Connect this to inflation
Inflation changes the spending power of money over time. Read the related inflation explainer, or explore historical market returns using your own assumptions.