Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This creates exponential growth over time, which Albert Einstein allegedly called "the eighth wonder of the world."

The compound interest formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of times interest compounds per year, and t is the time in years. For example, $10,000 at 5% annual interest compounded monthly for 10 years grows to $10,000 × (1 + 0.05/12)^(12×10) = $16,470.

The key difference from simple interest is significant over time. Simple interest of 5% on $10,000 for 10 years yields just $15,000. Compound interest yields $1,470 more because you earn interest on your interest. The longer the time period, the more dramatic this difference becomes.

How often interest compounds significantly affects your returns. The more frequently interest compounds, the more you earn. Daily compounding earns more than monthly, which earns more than annual compounding.

At 5% annual rate on $10,000 over 10 years: Annual compounding yields $16,289. Monthly compounding yields $16,470. Daily compounding yields $16,487. The difference of about $200 seems small, but with larger amounts and longer timeframes, it grows substantially.

Most savings accounts compound daily but post interest monthly. Investments like stocks don't technically compound at a set frequency — they grow based on market performance. However, dividend reinvestment creates a compounding effect. When comparing financial products, check both the stated interest rate and compounding frequency to understand true returns.

The Rule of 72 is a quick way to estimate how long it takes to double your money. Simply divide 72 by the annual interest rate. At 6% interest, your money doubles in approximately 72/6 = 12 years. At 8%, it takes about 9 years.

This rule works reasonably well for interest rates between 2% and 12%. For higher rates, use 69.3 instead of 72 for better accuracy. For very low rates, the rule slightly underestimates doubling time.

The Rule of 72 demonstrates the power of compound interest for long-term investing. Starting early is crucial because of how compounding accelerates over time. An investor who starts at age 25 and stops at 35 (10 years of contributions) can end up with more money than someone who starts at 35 and invests for 30 years, assuming similar returns. Use this calculator to see exactly how your money grows over different time periods and interest rates.