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Investopedia's Return on Investment (ROI) page says:

ROI can be used in conjunction with Rate of Return, which takes in account a project’s time frame

From this I understood that Return on Investment and Rate of Return are different formulas. They are two different measures. But in the Rate of Return (RoR) page, it says:

This simple rate of return is sometimes called the basic growth rate, or alternatively, return on investment, or ROI.

The second quote I have given from Investopedia ROR page contradicts the first quote from the ROI page. Moreover, the word "return on investment" is linked to the ROI page mentioned in the first line.

I am confused. Can anybody confirm that both are the same? If not, what are the formulas for these two measures and the differences between them?

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ROI (Return on Investment) is a simple percentage.

https://investinganswers.com/financial-dictionary/technical-analysis/return-investment-roi-1100

The return on investment formula is:

ROI = (Net Profit / Cost of Investment) x 100

But the word "rate" in ROR (Rate of Return) means that it involves time.

https://investinganswers.com/financial-dictionary/investing/rate-return-5875

Compounded annual growth rate (CAGR) is a common rate of return measure that represents the annual growth rate of an investment for a specific period of time.

The formula for CAGR is:

CAGR   =   (EV/BV)^(1/n) - 1

where:
EV = The investment's ending value
BV = The investment's beginning value
n  = Years

For example, let's assume you invest $1,000 in the Company XYZ mutual fund, and over the next five years, the portfolio looks like this:

End of Year    Ending Value
1              $  750
2              $1,000
3              $3,000
4              $4,000
5              $5,000

Using this information and the formula above, we can calculate that the CAGR for the investment is:

CAGR = ($5,000/$1,000)^(1/5) - 1 = .37972 = 37.97%

The simple ROI on this investment would be:

(5000 - 750)/750 * 100 = 566.67%
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  • The costs are 1k, wether you calculate the CAGR or the ROI. Hence, the ROI is (5000-1000)/1000*100. I dont know why this answer has not been corrected yet over such a long period of time. – shenflow Oct 24 '20 at 7:00
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Return on Investment is simply your profit as a percentage of what you put in. For instance, if you put in $100 and get $115 back, then you have $15 of profit, which is a ROI of 15%.

Rate of Return is the interest rate that an investment would have to pay to match the returns. In the previous example, if it took you two years to get your money back, then that's equivalent to an interest rate of 7.23%: with compounding over two years, an interest rate of 7.23% would give you 15% of the principal in interest.

If you get the return on the investment at a fixed time, the RoR is relatively simple to calculated; it's simply (1+RoI)^(1/n), where n is the number of years it takes to get your money back. But if you have a stream of payments at different times, then the calculation is more complicated. In fact, in some cases it's not uniquely defined.

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