Memorize these and you understand compound interest, the power of starting early, the savings-rate tradeoff, and what a million dollars actually means. The math is not complicated. It just has to be understood deeply.
READING TIME: 10 MIN
$1 at 7% real for 40 years becomes $15. $500/month at 7% for 40 years becomes $1.3M. Starting at 22 vs 32 with the same contributions produces roughly double the outcome at 62. A $1M portfolio at 4% withdrawal generates $40K/year indefinitely. The savings rate determines years to financial independence more than the investment return does.
Personal finance is not complicated at its core. Most of it reduces to six numbers. Understand these and the strategy follows.
Divide 72 by your expected annual return. The result is how many years it takes to double your money.
This is the number that makes the credit card balance graphic. It is also the number that makes "start early" obvious.
$1 invested at 7% real return for 40 years = approximately $15 (1.07^40 = 14.97). $1 invested at 10% nominal for 40 years = approximately $45 (1.10^40 = 45.26).
$500/month invested at 7% real:
| YEARS | BALANCE |
|---|---|
| 10 years | $86,400 |
| 20 years | $259,000 |
| 30 years | $566,000 |
| 40 years | $1,312,000 |
$1,000/month at 7% real for 30 years: $1,130,000. The number most people remember: $500/month for 40 years at 7% real = over a million dollars.
Starting at 22 versus 32 with identical contributions. Same $500/month. Same 7% return. Stop contributing at 62 in both cases.
Difference: $746,000. The cost of the first 10 years of contributions: $60,000 (120 months × $500). The compounding lost on those 10 years over the remaining decades: $686,000. The first decade of investing is the most valuable decade. This is why someone who starts at 22 and stops at 32 often ends up with more than someone who starts at 32 and never stops.
$1,000,000 portfolio. 4% annual withdrawal. $40,000/year, inflation-adjusted. Historically, the money lasts 30+ years 🔍 verify×DON'T TRUST, VERIFYClaim: The 4% safe withdrawal rate originates in Bengen (1994) backtesting US stock/bond portfolios over rolling 30-year windows.Verify at: Bengen in Journal of Financial Planning ↗Also replicated and updated by the Trinity Study and Bill Bengen's subsequent work. See ERN SWR series ↗ for longer horizons and failure cases..
Adjust for longer horizons: 30-year retirement, 4% is fine. 50-year early retirement, 3 to 3.5% is safer (28x to 33x expenses). Adjust for reliable income sources: Social Security, pensions, and part-time income reduce the portfolio target.
This is the most powerful single table in personal finance. Assumes 5% real return and a 4% safe withdrawal rate 🔍 verify×DON'T TRUST, VERIFYClaim: Years-to-FI derived from savings rate, assuming constant real return and constant savings rate, starting from zero.Verify at: Mr. Money Mustache, "Shockingly Simple Math of Early Retirement" ↗The original published-form of this table. Assumptions: spend all of non-saved income, invest all of saved income, 5% real return, 4% SWR. Actual numbers depend on starting balance..
| SAVINGS RATE | YEARS TO FINANCIAL INDEPENDENCE |
|---|---|
| 10% | 51 years |
| 20% | 37 years |
| 30% | 28 years |
| 40% | 22 years |
| 50% | 17 years |
| 60% | 12.5 years |
| 70% | 8.5 years |
The insight: going from 10% to 20% savings rate cuts 14 years off your working life. Going from 20% to 30% cuts 9 more. The leverage is highest at lower rates. Your savings rate matters more than your investment return in the first two decades.
These numbers assume consistent investment at the stated return. They do not guarantee a specific outcome. They show the relationship between savings rate and time, which is the most important relationship in personal finance. Run your specific numbers in the Savings Rate to FI Calculator.
The math does not require a financial advisor. It requires consistency.
Last updated 2026-04-22. Not financial advice. Real-return and SWR assumptions are historical; past returns do not guarantee future returns.