It is FALSE that if you invest at a rate of r for two periods, under compounding, your investment will grow to (1 r)2 per dollar invested.
This brings us to the idea of compounding interest in future value calculations.
The idea of compounding interest is that the rate of growth of your present investment for some periods will ensure that your investment grows to (1 + r)^n per dollar invested. Compound interest means that interest is also earned on the reinvested interest.
Thus, what is true is that if you invest at a rate of r for two periods, under compounding, your investment will grow to (1 + r)^2 per dollar invested and not (1 r)2.
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