Calculate ROI (total return) and CAGR (compound annual growth rate) from an investment's start and end values, over years or between two dates.
Cập nhật Ví dụ đã kiểm tra: 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.
| Năm | Giá trị | 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.
Nguồn đối chiếu: Python decimal: 1.65^(1/5) − 1 = 10.5342296%
Nguồn đối chiếu: Python datetime: 1,827 days / 365.25 = 5.0020534 years; 2^(1/5.0020534) − 1 = 14.8632986%
Nguồn đối chiếu: 365 days / 365 = 1 year, so CAGR equals ROI (definition)
Nguồn đối chiếu: 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.
Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 6. Ví dụ, “10,000 to 16,500 in 5 years” được kiểm tra bằng Python decimal: 1.65^(1/5) − 1 = 10.5342296%.
Microsoft Excel RRI function (equivalent interest rate for growth); CFA Institute — Quantitative Methods: The Time Value of Money (annualized returns).
Chỉ dùng để lập kế hoạch. Bên cho vay, cơ quan thuế và thị trường áp dụng cách làm tròn, phí và quy tắc riêng; hãy xác nhận số liệu với họ trước khi cam kết.
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