Understanding the Power of Compound Interest
Albert Einstein famously referred to compound interest as the "eighth wonder of the world," adding that "he who understands it, earns it; he who doesn't, pays it." Unlike simple interest—which only generates returns on your original principal—compound interest allows your earned interest to generate its own interest over successive periods.
Over long investment horizons (10, 20, or 30+ years), compounding creates an exponential growth curve (hockey stick effect), where the total interest earned far surpasses the total money you originally deposited out of pocket.
The Mathematical Compound Interest Formula
The fundamental formula used by banks, asset managers, and our calculator for single-sum compounding is:
Frequently Asked Questions (FAQ)
How does APY differ from APR?
APR (Annual Percentage Rate) reflects the simple annualized interest rate without taking compounding into account. APY (Annual Percentage Yield) includes the compounding effect, showing the true total return you earn over a full 12-month year. APY is always equal to or higher than APR.
What is the Rule of 72?
The Rule of 72 is a quick mental math shortcut used to estimate how many years it takes to double your money. Divide 72 by your expected annual rate of return. For example, at an 8% return, your money doubles in approximately 72 ÷ 8 = 9 years.
What typical annual return should I assume for US stock index funds?
Historically, broad US market index funds like the S&P 500 have averaged an annualized nominal return of approximately 10% over the last century (or roughly 7% when adjusted for inflation). Past performance is not a guarantee of future returns.