Finance
Compound Interest: The Most Powerful Formula in Personal Finance
If you understand one piece of math in personal finance, make it compound interest. Two investors saving the same total amount can finish 30 years apart in net worth — purely based on when they started.
The Formula
A = P × (1 + r/n)n×t
- A = final amount
- P = principal (starting amount)
- r = annual interest rate (decimal)
- n = compounding periods per year
- t = number of years
For monthly contributions, use the future value of an annuity formula. Our Compound Interest Calculator handles both cases.
Compounding Frequency
- Annual: simplest, slightly lower returns.
- Monthly: standard for US savings, mortgages, and 401(k) contributions.
- Daily: most US savings accounts and credit cards. Adds about 0.05–0.10% to effective yield versus monthly.
- Continuous: theoretical maximum, used in academic finance: A = P × ert.
The Rule of 72
Years to double your money ≈ 72 ÷ annual return. At 8%, money doubles every 9 years. At 12%, every 6 years. It’s a great mental check on any investment claim.
Time Beats Rate (Almost Always)
Investor A invests $5,000/year from age 25 to 35, then stops. Investor B invests $5,000/year from age 35 to 65. Both earn 8% annually.
- Investor A total contributed: $50,000. Value at 65: ~$615,000.
- Investor B total contributed: $150,000. Value at 65: ~$566,000.
Investor A puts in one third as much money and ends with more. That’s the entire argument for starting young.
Real-World Returns to Plan With (US, 2026)
- S&P 500 historical real return: ~7% after inflation
- 60/40 portfolio: ~5% real
- HYSA / 4-week T-Bills: 4–5% nominal (varies with Fed)
- I-Bonds: CPI + small fixed component
Always plan in real (inflation-adjusted) returns when modeling retirement.
Worked Example: Roth IRA Maxer
You contribute the 2026 Roth IRA max of $7,000/year for 40 years, earning 7% real return.
- Total contributed: $280,000
- Final balance: ~$1.49 million (real dollars)
- Roth advantage: tax-free withdrawal in retirement
FAQs
Does the bank really compound daily? Yes for most US savings products. The rate quoted is APY, which already includes compounding.
What return should I assume for retirement planning? 6–7% real for a stock-heavy portfolio. Lower assumptions = safer plan.
Is compound interest the same as APY? APY is the result of compound interest expressed as one annual number. APR ignores compounding.