# ROI and CAGR calculator

> Calculate ROI (total return) and CAGR (compound annual growth rate) from an investment's start and end values, over years or between two dates.

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분야: 금융 계산기

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.

## 입력

- **Amount invested**
- **Final value**
- **Income received along the way**: Dividends, interest or rent you took out. It is added to the final value.
- **Holding period from** (선택 항목: 년, 날짜)
- **Years held**
- **Bought on**
- **Valued on**
- **Days per year** (선택 항목: 365.25 (average year), 365 (as Excel XIRR))

## 결과

- CAGR (annualized return) — 주요 결과
- Total return (ROI)
- Gain
- Growth multiple (×)
- Holding period (years)

## 공식

$$
ROI = \frac{V_{end} + I - V_0}{V_0},\qquad CAGR = \left(\frac{V_{end} + I}{V_0}\right)^{1/t} - 1
$$

## 계산 예제

### 10,000 to 16,500 in 5 years

- Amount invested: 10,000
- Final value: 16,500
- Income received along the way: 0
- Holding period from: 년
- Years held: 5 years
- **Total return (ROI): 65%**
- **CAGR (annualized return): 10.53423%**
- **Gain: 6,500.00**
- 검증 출처: Python decimal: 1.65^(1/5) − 1 = 10.5342296%

### Doubling between two dates

- Amount invested: 10,000
- Final value: 20,000
- Income received along the way: 0
- Holding period from: 날짜
- Bought on: 2020-01-01
- Valued on: 2025-01-01
- Days per year: 365.25 (average year)
- **Holding period: 5.002053 years**
- **CAGR (annualized return): 14.863299%**
- **Total return (ROI): 100%**
- 검증 출처: Python datetime: 1,827 days / 365.25 = 5.0020534 years; 2^(1/5.0020534) − 1 = 14.8632986%

### Exactly one year, 365-day basis

- Amount invested: 100
- Final value: 110
- Income received along the way: 0
- Holding period from: 날짜
- Bought on: 2023-01-01
- Valued on: 2024-01-01
- Days per year: 365 (as Excel XIRR)
- **Holding period: 1 year**
- **CAGR (annualized return): 10%**
- **Total return (ROI): 10%**
- 검증 출처: 365 days / 365 = 1 year, so CAGR equals ROI (definition)

### Income taken out counts toward the return

- Amount invested: 1000
- Final value: 1100
- Income received along the way: 50
- Holding period from: 년
- Years held: 2 years
- **Total return (ROI): 15%**
- **CAGR (annualized return): 7.238053%**
- 검증 출처: Python decimal: √1.15 − 1 = 7.2380529%

### Microsoft RRI example

- Amount invested: 10,000
- Final value: 11,000
- Income received along the way: 0
- Holding period from: 년
- Years held: 96 years
- **CAGR (annualized return): 0.099331%**
- 검증 출처: Microsoft RRI documentation: RRI(96, 10000, 11000) = 0.0009933; Python decimal 0.0993307376%

### Total loss

- Amount invested: 1000
- Final value: 0
- Income received along the way: 0
- Holding period from: 년
- Years held: 3 years
- **CAGR (annualized return): -100%**
- **Total return (ROI): -100%**
- **Growth multiple: 0.0000 ×**
- 검증 출처: 0^(1/3) − 1 = −1 (definition)

## 자주 묻는 질문

### How do you calculate ROI?

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%.

### How do you calculate CAGR?

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.

### What is the difference between ROI and CAGR?

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.

### Is CAGR the same as the average annual return?

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.

### Should I use CAGR for a holding period under 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.

### “ROI and CAGR calculator”의 정확도는 어느 정도인가요?

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.

### 이 계산 방법의 출처는 무엇인가요?

Microsoft Excel RRI function (equivalent interest rate for growth); CFA Institute — Quantitative Methods: The Time Value of Money (annualized returns).

## 출처

- [Microsoft Excel RRI function (equivalent interest rate for growth)](https://support.microsoft.com/office/rri-function-6f5822d8-7ef1-4233-944c-79e8172930f4)
- CFA Institute — Quantitative Methods: The Time Value of Money (annualized returns)

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