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Multiply Over Time

How Compound Interest Works

Compound interest is interest calculated on both your initial principal and the interest already accumulated. Unlike simple interest (which only earns on the original amount), compound interest snowballs over time — and the longer you wait, the faster it grows.

The Formula Behind the Numbers

The compound interest formula is: A = P(1 + r/n)^(nt), where P is principal, r is annual interest rate, n is compounding periods per year, and t is years. Monthly compounding (n=12) yields slightly more than annual compounding on the same rate because interest is reinvested more frequently.

The Rule of 72

A quick mental math trick: divide 72 by your annual return rate to estimate how many years it takes to double your money. At 8% returns, your investment doubles every 9 years. At 6%, every 12 years. This is why starting early matters so much — an investment that doubles three times turns $10,000 into $80,000.

Why Monthly Contributions Change Everything

A lump sum benefits from compound interest, but regular monthly contributions are often more powerful for real investors. Contributing $500/month at 8% for 30 years produces $745,000 — more than 8× what you put in. The math works because each contribution has its own compounding runway, and early contributions have the longest time to grow.

Average Stock Market Returns: What to Expect

The S&P 500 has returned an average of approximately 10% annually before inflation since 1926. After inflation (historically ~3%), the "real" return is closer to 7%. Most financial planners use 6–8% as a conservative long-term assumption. Individual years vary wildly — the market dropped 37% in 2008 and returned 32% in 2013 — but long-term averages have been remarkably consistent.

Tax-Advantaged Accounts Amplify Compounding

Investing inside a 401(k) or IRA removes the drag of annual taxes on dividends and capital gains. A taxable account earning 8% might effectively earn 6.5% after taxes. Over 30 years on $200,000, that difference compounds to over $150,000 in additional wealth. Max out tax-advantaged accounts first before investing in taxable brokerage accounts.