$\"\"$

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The principal amount $\"\"$ .

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The rate of interest $\"\"$ .

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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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Take 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 $\"\"$ in the above equation.

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$\"\"$

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The amount double in $\"\"$ .

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$\"\"$

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The principal amount $\"\"$ .

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The rate of interest $\"\"$ .

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The period of time $\"\"$ .

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

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The total amount is

\

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$\"\"$

\

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The total amount after $\"\"$ is $\"\"$ .

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$\"\"$

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The amount double in $\"\"$ .

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The total amount after $\"\"$ is $\"\"$ .