Compound interest measures how savings grow when interest is paid not only on the original deposit but also on accumulated interest. The standard formula is A = P(1 + r/n)^(n t) where A is the account balance after t years, P is the principal, r is the annual interest rate expressed as a decimal, and n is the number of compounding periods per year; in the limit of continuous compounding the balance follows A = P e^{r t}. Financial educators and regulators use these expressions to explain returns: FDIC staff Federal Deposit Insurance Corporation and the Board of Governors Federal Reserve System describe these relationships in consumer guidance and explain how annual percentage yield reflects compounding frequency.
How the formula works
Frequent compounding increases growth because each period's interest becomes part of the base for the next period. The three drivers are the rate, the frequency of compounding and time. Small differences in rate or compounding frequency can produce materially different outcomes over decades, which is why the mathematics matters for retirement saving, education funds and long-term community investment. Mathematically, compounding is an exponential process, and the role of time makes patience a practical advantage for households and institutions that save regularly.
Practical implications for savers and communities
Beyond individual accounts, compound interest shapes broader economic patterns. Scholars studying capital and inequality point to the cumulative power of returns in shaping wealth concentration over long horizons; Thomas Piketty Paris School of Economics discusses how persistent differences in rates of return can affect distribution of wealth across generations. In territorial and cultural contexts where saving practices are embedded in family systems or local credit cooperatives, the mechanics of compounding interact with social norms and access to banking, producing distinctive outcomes for regional development.
Real-world effects and calculation in practice
To calculate a savings balance for a given account, substitute the known principal, quoted annual rate and the compounding frequency into A = P(1 + r/n)^(n t) and compute the exponent. Institutions emphasize that advertised rates may be quoted differently and that taxes, fees and account terms alter net results; CFPB staff Consumer Financial Protection Bureau and IRS staff Internal Revenue Service provide guidance showing how taxes and fees reduce effective returns. Understanding the formula enables informed choices about account types, compounding schedules and the long-term consequences of saving behavior.
