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Steady growth over several periods

Mental mathHard

An amount of $2000$ grows at a steady $10%$ per period. What is it after $4$ periods, exactly?

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Hint

Square the multiplier twice.

Solution

$1. 1^{2} = 1.21$ .
$1.2 1^{2} = 1.4641$ , since $1.21 \times 1.21 = 1.21 \times 1.2 + 1.21 \times 0.01 = 1.452 + 0.0121$ .
So $2000 \times 1.4641 = 2 \times 1464.1$ .
The amount is $2928.2$ .

Answer: $2928.2$