Step 1:

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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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$\"\"$

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Apply ln on each side.

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$\"\"$

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Using 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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$\"\"$ years.

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Step 2:

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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 10 years $\"\"$ $.

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Solution:

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Initial investment	Annual rate	Time to double	Amount after 10 years
$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$

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