$\"\"$

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(a)

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Consider Principal income is $\"\"$ .

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The total investment is $\"\"$ .

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Rate of interest is $\"\"$ .

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Compound interest formula: $\"\"$ .

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For monthly compounded $\"\"$ .

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Substitute the corresponding values in the formula.

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$\"\"$

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$\"\"$

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Apply logarithm on each side.

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$\"\"$

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Apply logarithm power rule property : $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The time period is $\"\"$ years.

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$\"\"$

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(b)

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Consider Principal income is $\"\"$ .

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The total investment is $\"\"$ .

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Rate of interest is $\"\"$ .

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$\"\"$ .

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Substitute all the values in the equation.

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$\"\"$

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$\"\"$

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Apply logarithm one to one property : if $\"\"$ ,then $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The time period is $\"\"$ years.

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$\"\"$

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(a) The time period is $\"\"$ years.

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(b) The time period is $\"\"$ years.