Calculate ROI (total return) and CAGR (compound annual growth rate) from an investment's start and end values, over years or between two dates.
업데이트 검증한 예제: 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.
| 년 | 값 | 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.
검증 출처: Python decimal: 1.65^(1/5) − 1 = 10.5342296%
검증 출처: Python datetime: 1,827 days / 365.25 = 5.0020534 years; 2^(1/5.0020534) − 1 = 14.8632986%
검증 출처: 365 days / 365 = 1 year, so CAGR equals ROI (definition)
검증 출처: 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.
정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 6. 예를 들어 “10,000 to 16,500 in 5 years”은 Python decimal: 1.65^(1/5) − 1 = 10.5342296%와 대조해 확인합니다.
Microsoft Excel RRI function (equivalent interest rate for growth); CFA Institute — Quantitative Methods: The Time Value of Money (annualized returns).
계획을 위한 참고용입니다. 대출기관, 세무당국과 시장은 자체 반올림 방식, 수수료와 규칙을 적용합니다. 계약 등의 결정을 내리기 전에 해당 기관에 수치를 확인하세요.
이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 6개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.
초기 예금과 정기 납입금의 미래 가치를 계산합니다. 일 복리와 연속 복리를 포함한 모든 복리 주기를 지원합니다.
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