compoundinterest

Compound interest is a method of calculating the growth of an investment or loan by adding accrued interest to the principal, so that future interest is earned on both the original amount and the previously accumulated interest. This process can be expressed mathematically as A = P(1 + r/n)^{nt}, where A is the amount after time t, P is the initial principal, r is the nominal annual interest rate expressed as a decimal, n is the number of compounding periods per year, and t is the number of years. When interest is compounded continuously, the formula becomes A = Pe^{rt}, using the base of natural logarithms e.

The frequency of compounding affects the final amount: more frequent compounding periods (daily, hourly, or continuously) result in larger totals compared with annual compounding, all else equal. The concept is fundamental in finance, affecting savings accounts, bonds, mortgages, and investment vehicles such as mutual funds and retirement plans. It also underlies the calculation of present and future values in discounted cash flow analysis.

Historical use of compound interest dates back to ancient civilizations, with evidence in Babylonian and Roman records. The formal mathematical treatment emerged during the Renaissance, notably through the work of mathematicians such as Jacob Bernoulli, who studied the limiting case leading to continuous compounding.

Critics sometimes view compound interest as contributing to wealth inequality because it can amplify the growth of capital over time. Regulations in some jurisdictions limit the maximum allowable rates for certain consumer loans to protect borrowers. Understanding compound interest is essential for personal financial planning, investment strategy, and evaluating long‑term economic outcomes.