$\"\"$ \ \

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The principal amount $\"\"$ .

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Amount after $\"\"$ is $\"\"$ .

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Formula for continuous compounding: $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Apply ln on each side.

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$\"\"$

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$\"\"$

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Substitute the value of $\"\"$ .

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$\"\"$

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$\"\"$ .

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The rate of interest $\"\"$ .

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$\"\"$

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The amount is doubled in $\"\"$ years.

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The amount $\"\"$ .

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Compounded continuously.

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Formula for continuous compounding: $\"\"$ .

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$\"\"$

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$\"\"$

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Apply ln on each side.

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$\"\"$

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Apply power rule of logarithms: $\"\"$ .

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$\"\"$

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Substitute the value of $\"\"$ .

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$\"\"$

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$\"\"$ \ \

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$ .

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$\"\"$

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Initial investment	Annual rate	Time to double	Amount after $\"\"$ years
$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$

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