Simple interest pays the same amount every period because it is always calculated on the starting sum. Compound interest recalculates on the growing balance, so each period's interest begins earning in turn. The SEC's investor.gov glossary walks a small deposit through two years to show the second year's interest edging past the first, and its calculator lets readers watch the gap widen over decades. The curve is gentle early and steep late, and that is the practical lesson: the largest yearly gains arrive at the end of a long horizon, so interrupting the process early costs far more than it seems to at the time.
- Rate: a higher rate compounds faster, and small differences widen over long terms.
- Frequency: interest credited monthly or daily grows slightly faster than the same nominal rate credited yearly, which is why annual equivalent figures are quoted for comparison.
- Time: the exponent in the formula; doubling the term more than doubles the interest earned.
- Withdrawals and fees: money taken out stops compounding, and a recurring charge compounds against the saver.
- Inflation: the Bank of England treats real rates as nominal rates adjusted for expected inflation, and the real rate is the one that describes growth in purchasing power.
Where it connects
Compound interest is the everyday face of the time value of money, run forwards instead of discounted back, and it is the reason net present value calculations divide by a rate raised to a power. It drives long-term personal finance and planning, where low costs in an index fund matter precisely because a fee behaves like a negative rate that compounds for as long as the money stays invested.