Compound Interest

How compound interest works

With simple interest, interest is calculated on the original principal. With compound interest, previously credited interest stays in the balance and can earn further interest. Investor.gov explains this distinction in its guide to small savings and compounding.

Suppose $1,000 earns a fixed 5% annually, with no withdrawals, fees or taxes. It earns $50 in the first year, leaving $1,050. The second year's interest is $52.50, leaving $1,102.50. Simple interest at the same rate would leave $1,100 after two years. The $2.50 difference is interest on the first year's interest.

Compound interest formula

For a constant nominal annual rate and regular compounding, A = P × (1 + r/n)^(n × t). Here A is the ending balance, P is the initial principal, r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the number of years. At 5%, use 0.05 rather than 5. This basic expression assumes no additional contributions or withdrawals.

For $1,000 at a 5% nominal annual rate compounded monthly for one year, the result is about $1,051.16. The effective annual growth is about 5.12%. If a quoted rate already represents an effective annual yield, do not divide that yield by 12 and treat it as a nominal monthly rate.

Contributions and timing

Regular deposits add a second source of balance growth. Each deposit compounds only for the time it remains invested, so depositing at the beginning of a period differs from depositing at its end. Separate money contributed from growth when reading a projection.

The Investor.gov compound interest calculator lets users set the initial balance, monthly contribution, duration, estimated rate, rate range and compounding frequency. Our compound interest calculator provides another way to explore a scenario with editable assumptions.

Investment compounding is uncertain

A fixed-rate example illustrates arithmetic, not a stock-market promise. Stock returns change from year to year and may be negative. A 20% rise followed by a 20% fall leaves $100 at $96, even though the arithmetic average return is zero. CAGR summarizes the annualized change between endpoints; it does not guarantee that rate in future years.

Fees, taxes, withdrawals and inflation also affect the result. A larger nominal balance does not necessarily mean the same increase in purchasing power. Compare several assumptions and label them as scenarios, especially when projecting decades into the future.