How Compound Interest Works
Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. This creates a snowball effect where your money grows faster over time — often called "the eighth wonder of the world."
Where A = final amount, P = principal, r = annual rate, n = compounds per year, t = years, PMT = periodic contribution.
Simple vs. Compound Interest
- Simple interest: Calculated only on the original principal. Formula: I = P × r × t
- Compound interest: Calculated on principal + accumulated interest. Grows exponentially.
For example, $10,000 at 7% for 20 years: Simple interest yields $24,000. Compound interest (monthly) yields $40,387 — that's 68% more!
The Rule of 72
A quick way to estimate how long it takes to double your money: divide 72 by the interest rate. At 7%, your money doubles in approximately 72 ÷ 7 ≈ 10.3 years.
Compounding Frequency
The more frequently interest compounds, the more you earn. Daily compounding earns slightly more than monthly, which earns more than annually. The difference becomes more significant with higher rates and longer time periods.
Frequently Asked Questions
What's a realistic return rate? The S&P 500 has historically returned about 10% annually (7% after inflation). Savings accounts offer 4-5% in high-yield accounts. Bonds typically return 3-5%.
How often should I contribute? Regular contributions (dollar-cost averaging) reduce risk and maximize compound growth. Monthly contributions are most common.
Does compound interest apply to debt? Yes — compound interest works against you on loans and credit cards. Credit card interest compounds daily on unpaid balances, which is why paying off debt quickly is so important.