How is compound interest different from simple interest?

Simple and compound interest differ in how interest is calculated over time. Simple interest applies a fixed percentage only to the original principal. Compound interest applies interest to the principal and to interest that has already been added, producing exponential growth. The algebraic expressions commonly used are simple interest amount A equals principal P times one plus rate r times time t, and compound interest amount A equals principal P times one plus rate r over compounding frequency n raised to the power n times t. Continuous compounding is the limiting case that yields A equals P times e to the r t, a formulation discussed in financial mathematics by John C. Hull at the University of Toronto.

Simple interest: definition and mechanics
Simple interest calculates interest solely on the initial sum lent or invested. For short-term loans, vehicle financing, and certain bonds, simple interest is a straightforward way to determine cost or return because interest does not accumulate on prior interest. From a borrower's perspective, simple interest keeps total cost proportional to time. From a lender or investor perspective, simple interest yields linear returns that do not benefit from reinvestment. Financial educators such as Sal Khan at Khan Academy use simple interest examples to illustrate basic time value of money concepts before introducing compounding.

Compound interest: definition and mechanics
Compound interest reinvests earned interest so that each period's interest is calculated on a progressively larger base. The frequency of compounding — annually, quarterly, monthly, or daily — affects the effective annual rate, meaning nominal rates cannot be compared without accounting for compounding frequency. In practice, compounding can dramatically increase balances over long horizons. John C. Hull at the University of Toronto and standard textbooks on finance demonstrate how compounding underlies instruments from savings accounts to reinvested dividends and is fundamental to the pricing of many financial products.

Why the difference matters
The causes of the divergence between simple and compound outcomes are mathematical and behavioral. Mathematically, compounding produces exponential growth because interest itself becomes an earning asset. Behaviorally, reinvestment choices, institutional rules about compounding frequency, and regulatory disclosure standards determine how consumers experience interest. The consequences are wide ranging. For savers and investors, compounding magnifies long-term wealth accumulation and is central to retirement planning. For borrowers, compound interest can substantially increase repayment burdens over time, especially on revolving credit where interest compounds frequently.

Human and territorial nuances amplify these effects. Thomas Piketty at the Paris School of Economics has highlighted how returns on capital that compound over decades contribute to wealth concentration within societies. Central bank policy and national regulations influence nominal rates and compounding conventions, so the same nominal rate can have different real impacts across countries. Environmental and community investments can also benefit from compound returns when long-term gains are reinvested, supporting sustained funding for conservation or infrastructure projects. Understanding the technical distinction between simple and compound interest therefore has practical importance for personal finances, public policy, and economic equity.