Investment Return Formulas
Return on investment measures the total gain against what you put in, regardless of how long it took:
ROI = (Final value + Income − Cost) / Cost × 100
Compound annual growth rate turns that into a yearly rate, so investments held for different lengths of time can be compared fairly:
CAGR = (Ending value / Beginning value)^(1 / years) − 1
Buy for $5,000, sell for $8,200 after 4 years and collect $300 in dividends: ROI is 70%, but CAGR is about 14.2% a year. A 70% gain over 4 years and a 70% gain over 15 years are very different results; CAGR shows it.
Rule of 72: Divide 72 by the annual return percentage to estimate the number of years to double your investment. At 8% return, money doubles roughly every 9 years.
Why we show a range
Markets do not return the same amount every year. The S&P 500 averaged close to 10% a year since 1926, but individual years ranged from about −43% to +54%. Two people who invest the same amounts can end up with very different balances depending on when the good and bad years arrive.
The chart simulates 600 possible futures using your expected return and the typical volatility of the portfolio you picked. The typical line is the median outcome. The bad line is the 10th percentile, a result worse than 9 out of 10 simulations. The good line is the 90th percentile. Longer horizons narrow the range of average yearly returns, although the dollar range still widens.
Historical Asset Class Returns (approximate, before inflation)
| Asset Class | Avg Annual Return | Notes |
|---|---|---|
| US Large Cap Stocks (S&P 500) | ~10% | Long-run historical average since 1926 |
| US Small Cap Stocks | ~12% | Higher risk and volatility |
| International Developed Stocks | ~7-8% | Europe, Japan, Australia |
| Emerging Market Stocks | ~9% | Higher risk, higher potential |
| US Bonds (10yr Treasury) | ~4-5% | Lower risk, lower return |
| Real Estate (REITs) | ~8-9% | Includes dividend income |
| Cash / Savings Account | ~3-5% | High-yield savings, no market risk |
Subtract about 3 points for inflation to get real returns. The portfolio presets in the calculator use expected returns slightly below these long-run averages, as most professional forecasts for the next decade do.
Fees and taxes
A 1% yearly fee on a portfolio that returns 8% takes one eighth of your return every year, and over 30 years that compounds into roughly a quarter of the final balance. Broad index funds cost 0.03% to 0.2%. Invest through tax-advantaged accounts where you can: 401(k) and IRA in the US, ISA and SIPP in the UK. In a taxable account, dividends and realized gains are taxed along the way.
Disclaimer: Past returns do not guarantee future results. All investments carry risk. This calculator is for educational purposes only and does not constitute financial advice.