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The simplest interest rate one can define, called an effective interest rate over the period T, is just the rate of increase. The effective interest rate is the increase from the initial loan amount, 𝑋𝑋0, to the final amount, 𝑋𝑋𝑇𝑇, relative to 𝑋𝑋0.

𝑟𝑟𝑒𝑒 = 𝑋𝑋𝑇𝑇−𝑋𝑋0 𝑋𝑋0

Dividing by the initial loan amount removes the scale of the investment, so that the growth 𝑋𝑋𝑇𝑇−𝑋𝑋0 is not considered itself but is considered relative to the size of the loan. However, it does not correct for the length of the loan.

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