The compound interest formula calculates the interest earned on an investment over time, where interest is added to the principal amount. The formula is expressed as A = P(1 + r/n)^nt , where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the money is invested. This formula highlights the power of compounding, which allows investments to grow faster than simple interest. By reinvesting the interest earned, investors can increase their returns significantly over time, making it a crucial concept in finance and personal investing. Understanding compound interest can help individuals make informed decisions about their savings and investments.