Definition
Compound interest is interest calculated on both the original amount and the interest already added to it, so a balance grows faster over time than with simple interest.
How it works
With simple interest, you earn the same amount each year because interest is paid only on the original principal. With compounding, each period's interest is added to the balance, and the next period's interest is calculated on that larger amount. The standard formula is A = P × (1 + r ÷ n)^(n × t), where A is the final amount, P the principal, r the yearly rate as a decimal, n the number of compounding periods per year and t the number of years.
Time has the strongest effect, because growth builds on itself: the same rate adds more in later years than in early ones. More frequent compounding, such as monthly instead of yearly, raises the result slightly. A quick estimate is the rule of 72: years to double ≈ 72 ÷ annual rate in percent.
The formula assumes a constant rate and that all interest is reinvested. Real results also depend on fees, taxes and inflation, which reduce what you keep. Compounding works the same way on debt: when unpaid interest is added to a loan or card balance, the amount owed grows on itself.
Example (hypothetical numbers)
Suppose you deposit $3,000 at 6% a year, compounded monthly, and leave it for 15 years.
A = $3,000 × (1 + 0.06 ÷ 12)^(12 × 15) = $3,000 × 1.005^180 ≈ $3,000 × 2.4541 ≈ $7,362.28.
With simple interest, the total would be $3,000 + $3,000 × 0.06 × 15 = $5,700.
The rule of 72 estimates 72 ÷ 6 = 12 years to double; the exact formula gives about 11.6 years with monthly compounding.
Compounding added about $1,662.28 more than simple interest, mostly in the later years.
Common mistakes
- Expecting compound growth to look large in the first few years.
- Assuming a constant rate for decades, even though rates usually change over time.
- Ignoring fees, taxes and inflation when projecting a compounded balance.
- Forgetting that unpaid interest on debt compounds against you in the same way.
Related calculators
This glossary is for education only and is not investment advice. Examples use hypothetical numbers.