$\"\"$

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

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The compound interest can be calculated by the equation $\"\"$ .

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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)

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For annually compounded interest:

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

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$\"\"$

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Take natural logarithm on both sides.

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$\"\"$

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$\"\"$

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(b)

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For monthly compounded interest :

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

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$\"\"$

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Take natural logarithm on both sides.

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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)

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For daily compounded interest :

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

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$\"\"$

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Take natural logarithm on both sides.

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$\"\"$

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$\"\"$

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$\"\"$

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(d)

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For continously compounded interest :

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For compounded continously $\"\"$ .

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

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$\"\"$

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Take natural logarithm on both sides.

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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 continously compounded interest time is $\"\"$ .