The Power of Compound Interest: A Worked Example

Compound interest is interest on a growing balance. With no deposits or withdrawals, A = P × (1 + r/n)^(n×t), where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. The CFPB explains how adding interest to principal changes later interest. This is a mathematical model, not a promise about an investment.

At a hypothetical 7% compounded annually, $10,000 becomes $10,700 after one year and $11,449 after two. After 30 years with no further contributions, it becomes $76,122.55. Fees, taxes and inflation are excluded.

Compounding frequency matters when the nominal rate stays fixed. Over 20 years, $10,000 at 7% gives $38,696.84 annually, $40,387.39 monthly and $40,546.56 daily. APY already includes compounding; entering an APY as a nominal rate and compounding it again overstates the yield.

All growth examples below are hypothetical: a constant 7% nominal annual rate compounded monthly, end-of-month contributions, no withdrawals, and no fees, taxes or inflation adjustment. They are nominal future dollars, not forecasts or today’s purchasing power.

With zero starting principal and $200 contributed at each month-end, the modeled balances are $34,616.96 after 10 years, $104,185.33 after 20 and $243,994.20 after 30. Total contributions are $24,000, $48,000 and $72,000 respectively. The increase in balance between two dates includes new contributions as well as growth; it must not all be labeled interest.

For the same $200 month-end contribution, 40 years produces $524,962.68; 35 years produces $360,210.92. That illustrates one set of assumptions. It does not establish a universal percentage advantage for starting five years earlier.

When contributions are monthly, use the monthly yield q = (1 + r/n)^(n/12) − 1 and M = 12t payments. End-of-month future value is P(1+q)^M + C((1+q)^M−1)/q. If q is zero, the contribution term is CM. Beginning-of-month contributions earn one extra monthly growth period.

To reproduce the contribution example, enter principal 0, monthly contribution 200, annual rate 7, monthly compounding and end-of-month timing. Try lower or negative rates as well. For money needed on a fixed date, consider access, fees and loss risk rather than treating the chart as a schedule of future market performance.

Correction, October 29, 2026: examples, assumptions, FAQs and visuals were reviewed together. Unsupported current statistics and promises were removed. The stated calculations use independent high-precision references.