$\"\"$

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(a)

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The equation for the amount for annually compound interest is $\"\"$ .

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The amount is doubled, therefore $\"\"$ .

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Interest rate is $\"\"$ and principal $\"\"$ in $\"\"$ .

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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Time necessary for $\"\"$ to double at $\"\"$ for annually compunded interest is $\"\"$ years.

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$\"\"$

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(b)

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The equation for the amount for monthly compound interest is $\"\"$ .

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The amount is doubled, therefore $\"\"$ .

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For monthly compounding : $\"\"$ .

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Interest rate is $\"\"$ and principal $\"\"$ in $\"\"$ .

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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$\"\"$ .

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Time necessary for $\"\"$ to double at $\"\"$ for monthly compunded interest is $\"\"$ years.

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$\"\"$

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(c)

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The equation for the amount for daily compound interest is $\"\"$ .

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The amount is doubled, therefore $\"\"$ .

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For monthly compounding : $\"\"$ .

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Interest rate is $\"\"$ and principal $\"\"$ in $\"\"$ .

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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$\"\"$ .

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Time necessary for $\"\"$ to double at $\"\"$ for daily compunded interest is $\"\"$ years.

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$\"\"$

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(d)

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The equation for the amount for continuously compound interest is $\"\"$ .

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The amount is doubled, therefore $\"\"$ .

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Interest rate is $\"\"$ and principal $\"\"$ in $\"\"$ .

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$\"\"$

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Take natural logarithm on each side.

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$\"\"$

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$\"\"$

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Time necessary for $\"\"$ to double at $\"\"$ for continuously compunded interest is $\"\"$ years.

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$\"\"$

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(a) Time necessary for $\"\"$ to double at $\"\"$ annually compunded interest is $\"\"$ years.

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(b) Time necessary for $\"\"$ to double at $\"\"$ monthly compunded interest is $\"\"$ years.

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(c) Time necessary for $\"\"$ to double at $\"\"$ daily compunded interest is $\"\"$ years.

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(d) Time necessary for $\"\"$ to double at $\"\"$ continuously compunded interest is $\"\"$ years.