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INVESTING GUIDE 6 min read

What Is Compound Interest: The Eighth Wonder of the World

Albert Einstein reportedly called compound interest the "eighth wonder of the world." Learn why it is the most vital math concept in wealth accumulation.

What is Compound Interest?

Compound interest is the interest you earn on interest. This simple concept is the engine behind long-term wealth building. Unlike simple interest, which is calculated only on your initial principal, compound interest adds your earned interest back into the principal balance, meaning you earn interest on a larger balance next period.

The Mathematical Engine

The formula for compound interest is:

A = P(1 + \frac{r}{n})^{nt}

Where:

  • A = Future value of the investment
  • P = Principal amount (initial investment)
  • r = Annual interest rate (decimal)
  • n = Number of compounding periods per year
  • t = Total time in years

    • Why Compounding Frequency Matters

    The compounding frequency (n) determines how often interest is calculated. The more frequent the compounding, the higher your ultimate yield:

    1. Annually (n=1): Interest is calculated once a year. 2. Monthly (n=12): Interest is calculated 12 times a year, meaning you earn interest on your January interest in February. 3. Daily (n=365): The fastest standard rate of compounding, maximizing your yield.

    The Rule of 72

    A quick way to estimate the power of compounding is the Rule of 72. Divide 72 by your expected annual rate of return to find how many years it will take to double your money.

    For example:

  • At a 6% return, your money doubles in 12 years (72 / 6 = 12).
  • At an 8% return, your money doubles in 9 years (72 / 8 = 9).
  • At a 12% return, your money doubles in just 6 years (72 / 12 = 6).

    • How to Make Compounding Work for You

  • Start Early: The absolute most important variable is time. A dollar saved in your 20s is worth far more than a dollar saved in your 40s.
  • Keep Costs Low: Fees eat directly into your returns, compounding *against* you.
  • Reinvest Dividends: Let your dividends buy more shares, adding more fuel to your compounding engine.

    • Frequently Asked Questions

    What is the difference between simple and compound interest?

    Simple interest is calculated solely on the original principal. Compound interest is calculated on the principal plus any accumulated interest from previous periods.

    How does compounding frequency affect my savings?

    The more frequently interest compounds (e.g., daily vs. annually), the faster your wealth accumulates because you earn interest on earned interest sooner.