Compound interest is interest earned on interest. Each year, your investment grows by the expected return rate, and the next year's interest is calculated on the new (larger) balance. Over decades, this creates exponential growth — the kind of curve that looks flat for 10 years, then explodes upward.
The formula
For a single lump sum: FV = P × (1 + r)^n, where P is principal, r is annual rate, n is years.
For recurring monthly contributions, we use the future value of an annuity formula: FV = PMT × [((1 + r/12)^(12n) − 1) ÷ (r/12)], plus the lump-sum future value. We sum both for the total.
Why the inflation adjustment matters
A million dollars in 2055 will not buy what a million dollars buys today. Long-term U.S. inflation averages about 3% per year, which means prices double roughly every 24 years. The "real" return of an 8% nominal investment is closer to 5% after inflation. Always look at the inflation-adjusted number when planning for retirement — the nominal number will mislead you.
Reasonable return assumptions
The S&P 500 has averaged about 10% nominal returns since 1926, or about 7% real (after inflation). For planning, use 6-8% nominal (4-5% real) to be conservative. Bonds return 3-5% nominal. A 60/40 portfolio returns about 7% nominal. Anything promising 12%+ sustained returns is selling something.