What is compound interest and why Einstein called it the 8th wonder
Albert Einstein reportedly called compound interest the eighth wonder of the world. “He who understands it, earns it. He who doesn’t, pays it.” Whether or not the quote is authentic, the sentiment is right.
Compound interest explained simply
Compound interest is interest earned on interest. When you put money in a savings account or investment, you earn interest on your original deposit (the principal). Next period, you earn interest on the principal plus the interest you already earned. Your money snowballs.
Simple interest is linear. $10,000 at 5% simple interest earns $500 every year. After 10 years, you have $15,000.
Compound interest is exponential. $10,000 at 5% compounded annually earns $500 in year one, $525 in year two (5% of $10,500), $551.25 in year three, and so on. After 10 years: $16,288.95.
The difference is $1,288.95 — and it grows dramatically over longer periods.
The three levers of compounding
Three factors determine how powerful compounding is for you:
Time. This is the most important lever. A 25-year-old who invests $5,000/year for 10 years and stops will have more at 65 than a 35-year-old who invests $5,000/year for 30 years. That 10-year head start gives compounding 30 extra years to work.
Rate of return. A 1% difference in annual return compounds to a massive difference over decades. $10,000 at 6% for 40 years = $102,857. At 8% = $217,245. At 10% = $452,593.
Consistency. Regular contributions amplify compounding enormously. The person who invests $500/month consistently, even during market downturns, dramatically outperforms the person who tries to time the market.
The dark side: compound interest on debt
Compound interest works against you on debt. Credit cards at 22% APR compound daily. A $5,000 credit card balance with minimum payments takes over 15 years to pay off and costs more than $7,000 in interest. That is the eighth wonder working in reverse.
Use the Compound Interest Calculator to see how your money grows, and the Investment Return Calculator to compare different scenarios.
Frequently asked questions
What is compound interest?
Compound interest is interest earned on both your original principal and the accumulated interest from previous periods. Unlike simple interest, which only pays on the principal, compound interest grows exponentially because each period’s interest is added to the base that earns interest in the next period.
How do I calculate compound interest?
Use the formula A = P(1 + r/n)^(nt), where A is the final amount, P is principal, r is the annual rate, n is compounding frequency per year, and t is years. For $5,000 at 8% compounded monthly for 10 years: A = 5000(1 + 0.08/12)^(12×10) = $11,098. Use the Compound Interest Calculator to avoid manual math.
What is the rule of 72?
The rule of 72 is a shortcut to estimate how long it takes to double your money at a given rate. Divide 72 by your annual return rate. At 8% return, your money doubles in 72/8 = 9 years. At 6%, it takes 12 years. At 10%, it takes about 7.2 years. This rule works for annual returns between 4% and 15%.
How does compounding frequency matter?
The more frequently interest compounds, the faster your money grows. $10,000 at 8% annual rate grows to $21,589 with annual compounding, $21,673 with monthly compounding, and $21,725 with daily compounding over 10 years. The difference between monthly and daily is small, but switching from annual to monthly adds about $84 per $10,000.
How much can I earn with compound interest over 10 years?
Investing $10,000 at 8% compounded annually grows to $21,589 over 10 years — more than doubling your money. Add $200 monthly contributions and the total reaches $47,217. Over 30 years, that same $10,000 with $200/month grows to roughly $327,000 at 8% return.