$\"\"$

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The compounded amount function is $\"\"$ .

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Where the initital amount $\"\"$ is constant.

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Consider the function is $\"\"$ .

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Apply logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Evaluate of the limit .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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L $\"\"$ Hospital $\"\"$ s Rule :

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If the value of limit is indeterminate form of type $\"\"$ or $\"\"$ , then

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$\"\"$

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$\"\"$

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Since $\"\"$ use L $\"\"$ Hospital $\"\"$ s rule.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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Therefore as $\"\"$ tends to $\"\"$ , the compounded amount is $\"\"$ .

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$\"\"$

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$\"\"$ .