ROI and annualized ROI
ROI = (Final value − Invested) ÷ Invested Annualized ROI = (Final value ÷ Invested)^(1/years) − 1
If $1,000 grows to $1,500 over 2 years, ROI is 500 ÷ 1,000 = 50%. The annualized ROI is 1.5^(1/2) − 1 ≈ 22.5% a year, not 25%, because each year's gain builds on the last.
How to calculate ROI by hand
You put $12,000 into a project, including all fees, and after 3 years it is worth $15,600.
- Gain: 15,600 − 12,000 = $3,600.
- ROI: 3,600 ÷ 12,000 = 0.30, or 30% over the whole period.
- Growth multiple: 15,600 ÷ 12,000 = 1.3.
- Annualized ROI: 1.3^(1/3) − 1 ≈ 0.0914, or about 9.14% a year.
Dividing 30% by 3 years would give 10%, which overstates the yearly rate. The annualized figure is the steady compound rate that turns $12,000 into $15,600 in 3 years.
Why time changes the picture
| Invested | Final value | Years | ROI | Annualized ROI |
|---|---|---|---|---|
| $1,000 | $1,500 | 2 | 50% | 22.47% |
| $1,000 | $1,500 | 5 | 50% | 8.45% |
| $1,000 | $1,500 | 10 | 50% | 4.14% |
| $1,000 | $2,000 | 3 | 100% | 25.99% |
| $1,000 | $2,000 | 10 | 100% | 7.18% |
| $1,000 | $1,100 | 0.5 | 10% | 21.00% |
| $1,000 | $800 | 2 | −20% | −10.56% |
A 10% gain in six months annualizes to 21%, but only if you could repeat it. Short periods can make annualized figures look extreme, so read them with care.
Reading the result
- A negative ROI means a loss. A final value of zero is a −100% ROI.
- Annualized ROI needs an investment length above zero. It is the same as the compound annual growth rate (CAGR).
- Include every cost in the amount invested (fees, commissions, extra money put in later) and every return in the final value (dividends, interest, sale proceeds) for an accurate figure.
Common mistakes
- Ignoring time. A 50% ROI over 10 years is a weaker result than a 30% ROI over 2 years.
- Leaving out costs. Fees, maintenance and your own time all reduce the real return.
- Comparing different risks. Two investments with the same ROI are not equal if one could easily have lost money.