What is Compound Interest?

Compound interest is the interest calculated on the initial principal of a deposit or loan, plus all of the accumulated interest from prior periods. Often described as 'interest earned on interest,' this mechanism causes the total value of an investment or debt to grow at an accelerating, exponential rate over time rather than a linear one. The rate at which compounding drives growth is heavily influenced by the compounding frequency, which can occur daily, monthly, quarterly, semi-annually, or annually.

The mathematical formula used to calculate the future value of an investment with compound interest is: \(A = P(1 + r/n)^{nt}\). In this equation, 'A' represents the final future value, 'P' is the initial principal balance, 'r' is the annual interest rate, 'n' is the number of times interest compounds per year, and 't' is the total time in years. Because interest is added to the principal balance at the end of each compounding period, more frequent compounding intervals (such as daily compounding instead of annual compounding) yield higher total returns over the same period of time.

In personal finance, compound interest is the single most powerful driver of retirement savings and wealth accumulation. Over short horizons, the difference between simple and compound interest is minor; however, over multi-decade horizons (20 to 40 years), compounding creates an exponential growth curve, turning small, consistent contributions into significant nest eggs. Conversely, compound interest is also the mechanism that makes revolving credit card debt exceptionally expensive, as unpaid interest is added to the card balance, compounding the amount the consumer owes.