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Alternating moves on a basket

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A basket is worth $500$ . On consecutive days it moves by $- 10%$ , $+ 10%$ and $- 10%$ , each relative to the previous close. What is it worth after the last day?

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Hint

Keep each intermediate value; the pattern is not symmetric.

Solution

Opening day: $500 \times 0.9 = 450$ .
Next day: $450 \times 1.1 = 495$ .
Last day: $495 \times 0.9$ , which is $495 - 49.5$ .
The basket is worth $445.5$ .

Answer: $445.5$

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