Calculate ROI (total return) and CAGR (compound annual growth rate) from an investment's start and end values, over years or between two dates.
Aktualisiert Geprüfte Beispiele: 6
Turning $10,000.00 into $16,500.00 over 5 years is a total return of 65%, the same as 10.53% a year compounded.
| Jahr | Wert | Growth since previous row |
|---|---|---|
| 0 | $10,000.00 | $0.00 |
| 1 | $11,053.42 | $1,053.42 |
| 2 | $12,217.82 | $1,164.39 |
| 3 | $13,504.87 | $1,287.05 |
| 4 | $14,927.50 | $1,422.63 |
| 5 | $16,500.00 | $1,572.50 |
Income is treated as received at the end; reinvesting it earlier would change the rate slightly.
ROI is the total gain as a share of the amount invested: (final value + income − amount invested) ÷ amount invested. CAGR turns that into a steady yearly rate, (ending value ÷ amount invested)^(1/years) − 1: the rate that, compounded every year, would reach the same end value. Between two dates, the holding period is the actual number of days divided by 365.25, or by 365 as Excel's XIRR does.
With the defaults, 10,000 growing to 16,500 in 5 years is a 65% total return and a CAGR of 10.53% a year. Dividing 65% by 5 years gives 13%, which overstates the yearly rate because it ignores compounding.
Both figures treat the investment as one payment in and one value out. If you added or withdrew money along the way, use the XIRR calculator, which weights each cash flow by its date.
Prüfquelle: Python decimal: 1.65^(1/5) − 1 = 10.5342296%
Prüfquelle: Python datetime: 1,827 days / 365.25 = 5.0020534 years; 2^(1/5.0020534) − 1 = 14.8632986%
Prüfquelle: 365 days / 365 = 1 year, so CAGR equals ROI (definition)
Prüfquelle: Python decimal: √1.15 − 1 = 7.2380529%
Divide the gain by the amount invested and multiply by 100: ROI = (final value + income − cost) ÷ cost × 100. An investment of 10,000 now worth 16,500 has an ROI of 6,500 ÷ 10,000 = 65%. Income you took out counts too: 1,000 that grew to 1,100 and paid 50 of dividends returned 15%.
Divide the ending value by the starting value, raise the result to the power 1 ÷ years, and subtract 1. For 10,000 growing to 16,500 in 5 years, 1.65^(1/5) − 1 = 10.53% a year. In Excel, =RRI(5, 10000, 16500) returns the same rate.
ROI measures the whole gain and ignores time; CAGR spreads it over the years as a compound rate. A 65% ROI is a CAGR of 10.53% if it took 5 years but only 5.14% if it took 10 years. Use CAGR to compare investments held for different lengths of time.
No. The average of yearly returns ignores compounding, so it overstates the growth whenever returns vary. An investment that gains 50% one year and loses 50% the next has an average return of 0%, but it ends at 75% of its starting value, a CAGR of −13.40% a year.
With care, because CAGR assumes the same return would repeat for a full year. A 5% gain in 3 months annualizes to 1.05^4 − 1 = 21.55% a year, which says little about what the next nine months will bring. For short holdings the total return is the plainer figure.
Die Genauigkeit hängt von Ihren Eingaben und den Annahmen der Methode ab. Die Dezimalrechnung nutzt 50 signifikante Stellen, doch Schätzungen, numerische Verfahren und Quelldaten können ungenauer sein. Die angezeigte Rundung beseitigt diese Grenzen nicht. Anhand unabhängiger Quellen geprüfte Rechenbeispiele: 6. Beispielsweise wird „10,000 to 16,500 in 5 years“ anhand von Python decimal: 1.65^(1/5) − 1 = 10.5342296% geprüft.
Microsoft Excel RRI function (equivalent interest rate for growth); CFA Institute — Quantitative Methods: The Time Value of Money (annualized returns).
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Dieser Rechner enthält 6 Rechenbeispiele mit Ergebnissen aus unabhängigen Quellen. Sie laufen in der Testsuite und können auch hier ausgeführt werden.
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