$\"\"$ \ \

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The rate of interest $\"\"$ and principle amount is $\"\"$ .

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Apply the formula for compound interest is : $\"\"$ .

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Where $\"\"$ is number of times interest compounded in an year.

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

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The amount $\"\"$ .

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(a) For annually compounded interest :

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

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$\"\"$

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Apply natural logarithm on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b) For monthly compounded interest :

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

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$\"\"$

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Apply natural logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(c) For daily compounded interest :

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

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$\"\"$

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Apply natural logarithm on each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(d) For continuously compounded interest :

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

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

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$\"\"$

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Apply natural logarithm on each side.

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) For annually compounded interest time is $\"\"$ .

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(b) For monthly compounded interest time is $\"\"$ .

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(c) For daily compounded interest time is $\"\"$ .

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(d) For continuously compounded interest time is $\"\"$ . \ \