What Is Compound Interest?
Compound interest is interest earned on both your original principal and previously accumulated interest - 'interest on interest.' Unlike simple interest (calculated only on principal), compound interest grows exponentially over time. This makes it powerful for long-term savings: $1,000 at 7% compounds to $1,967 in 10 years vs $1,700 with simple interest.
Key Takeaways
- With simple interest, you earn the same amount each period.
- Compound interest works against you with debt - credit card balances grow quickly at 20%+ rates.
- Inflation reduces the real return - 7% nominal return with 3% inflation is about 4% real return.
Explanation
With simple interest, you earn the same amount each period. $1,000 at 10% simple interest earns $100 per year, every year. With compound interest, year one earns $100, but year two earns 10% of $1,100 = $110. Each year the interest amount grows because the base amount grows.
The frequency of compounding matters. Interest can compound annually, monthly, daily, or continuously. Monthly compounding earns slightly more than annual because interest starts earning interest sooner. The difference increases with higher interest rates and longer time periods.
The Rule of 72 provides a quick estimate: divide 72 by the interest rate to find how many years it takes to double your money. At 6% interest, money doubles in about 12 years. At 8%, about 9 years. Starting early dramatically increases wealth because of more time for compounding to work.
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times compounded per year, and t is the number of years. For example, $10,000 at 5% compounded monthly for 30 years becomes $44,677. The same amount with annual compounding produces $43,219. That $1,458 difference comes entirely from more frequent compounding, which is why savings accounts that compound daily earn slightly more than those compounding monthly.
The power of compound interest becomes dramatic over long periods. A 25-year-old who invests $200 per month at a 7% average annual return will have approximately $525,000 by age 65. A 35-year-old making the same investment will have only about $244,000. That extra decade of compounding more than doubles the outcome despite contributing only $24,000 more in total deposits. This is why financial advisors emphasize starting early, even with small amounts, rather than waiting until you can invest larger sums.
Things to Know
- Compound interest works against you with debt - credit card balances grow quickly at 20%+ rates.
- Inflation reduces the real return - 7% nominal return with 3% inflation is about 4% real return.
- Tax treatment affects actual returns - tax-advantaged accounts preserve more of the compounding benefit.
- Student loans and mortgages use different compounding methods. Federal student loans use simple daily interest, while most mortgages amortize interest monthly, which affects how extra payments reduce total cost.