$\"\"$

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(a)

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The formula is $\"\"$ .

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Double the value of an IRA means $\"\"$ .

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Compoundd annuallt.

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$\"\"$

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The rate of interest is $\"\"$ .

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Substitute all the values.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ years will it take to double the value of an IRA that compounds annually at the rate of $\"\"$ .

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$\"\"$

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(b)

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Triple the value of an IRA means $\"\"$ .

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For quartely compounded $\"\"$

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The rate of interest is $\"\"$ .

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Substitute all the values in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, $\"\"$ years will it take to double the value of an IRA that compounds annually at the rate of $\"\"$ .

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$\"\"$

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(c)

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Derive the formula $\"\"$ .

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Total amount is compound interest is $\"\"$ .

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When Fidn time to Time to Double or Triple an Investment then the multiple is $\"\"$ .

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Therefore, $\"\"$

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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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Therefore, $\"\"$ .

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$\"\"$

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(a) $\"\"$ years .

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(b) $\"\"$ years.

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(c) $\"\"$ .