Compound Interest
Calculator

Compound interest is interest earned on both your original principal and the interest already accumulated. Unlike simple interest (which only earns on the principal), compounding creates exponential growth — your interest earns interest. Einstein allegedly called it the "eighth wonder of the world." A $10,000 investment at 7% for 30 years grows to ~$76,000 with simple interest but ~$81,000 with annual compounding — and significantly more with monthly compounding or regular contributions.

The standard formula is: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is time in years. When you add regular contributions (C per period), the formula extends to include a geometric series: A = P(1 + r/n)^(nt) + C × [((1 + r/n)^(nt) − 1) / (r/n)]. This calculator applies the full formula including monthly contributions.

More frequent compounding = slightly more growth. Daily compounding is marginally better than monthly, which is better than annual. However, the differences are smaller than most people expect. At 7% for 20 years on $10,000: annual compounding gives $38,697; monthly gives $40,064; daily gives $40,135. The rate itself matters far more than the compounding frequency. Focus on getting a better rate — switching from 5% to 7% has a vastly larger impact than switching from annual to daily compounding at the same rate.

The US stock market (S&P 500) has historically returned about 10% annually before inflation, or roughly 7% after inflation, averaged over long periods. However, this varies enormously by decade — some 10-year periods return 15%+, others lose money. For conservative planning, 6–7% real return is a reasonable assumption for a diversified stock portfolio held 20+ years. Always stress-test your projections at lower rates (4–5%) to ensure your plan works in a pessimistic scenario.

The Rule of 72 is a quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes to double your money. At 6%: 72/6 = 12 years to double. At 9%: 72/9 = 8 years. At 12%: 72/12 = 6 years. It's surprisingly accurate for rates between 4% and 12%. You can also flip it: to double in 10 years, you need roughly 72/10 = 7.2% annual return.

Inflation erodes purchasing power over time. If your portfolio grows at 7% but inflation runs at 3%, your real return is only about 4%. This calculator shows both the nominal balance (raw dollars) and the inflation-adjusted real value (what that money can actually buy). For long-term planning, always focus on real returns. $500,000 in 30 years sounds impressive but at 3% annual inflation is worth only about $206,000 in today's dollars.

Dramatically — often more than the initial principal over long periods. Consider: $10,000 invested for 30 years at 7% grows to ~$76,000. Adding just $200/month adds another ~$227,000 to the final balance. The monthly contributions benefit from compounding for varying lengths of time (the early ones compound almost as long as the principal; the last ones barely compound at all), but the cumulative effect is enormous. This is why consistent investing — even small amounts — is so powerful over decades.