The standard formulas, with one worked example each.
| Measure | Formula | Example |
|---|---|---|
| Return on investment (ROI) | (Amount back − costs − amount in) ÷ amount in | $14,000 back, $200 costs, $10,000 in: 38% |
| Yearly return | (1 + ROI) ^ (1 ÷ years) − 1 | 38% over 4 years: 8.4% |
| CAGR | (End ÷ start) ^ (1 ÷ years) − 1 | $10,000 to $20,000 in 10 years: 7.2% |
| Doubling time | ln(2) ÷ ln(1 + rate) | At 7.2%: about 10 years |
| Rule of 72 | 72 ÷ rate as a number | At 8%: about 9 years |
| Real return | (1 + return) ÷ (1 + inflation) − 1 | 8% with 3% inflation: 4.9% |
| Net present value (NPV) | Sum of cash ÷ (1 + rate) ^ year, less amount in | Cash comes later, so each year counts for less |
| Internal rate of return (IRR) | The rate that makes NPV equal zero | $1,000 in, $300 a year for 5 years: 15.2% |
| Discounted cash flow (DCF) | Sum of future cash ÷ (1 + rate) ^ year, plus a terminal value | $5 cash a share, 9% discount rate, 8% then 5% growth, 2.5% after year 10: about $108 |
Calculators
Guides
The linked Investor.gov pages cover annual return and compound growth only. The other formulas are standard finance methods. These are estimates for learning. They do not predict future returns or tell you what to buy.
CAGR calculator Try the CAGR calculator.Sources
- Background reading, Investor.gov: Annual return
- Background reading, Investor.gov: Compound interest
- Background reading, Investor.gov: Compound interest calculator
This article is for education and is not financial, tax or legal advice. Figures are checked against the sources above and may change. Read the full disclaimer.