$\"\"$

\

The principal amount $\"\"$ .

\

The amount after ten years is $\"\"$ .

\

Hence time period is $\"\"$ .

\

Find the rate of interest for continuously compounded interest.

\

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

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Take natural logarithm on both sides.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ . \ \

\

Therefore, the annual rate of interest is $\"\"$ .

\

$\"\"$

\

Find the time to double the amount.

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

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

\

The amount $\"\"$ .

\

$\"\"$ \ \

\

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

\

$\"\"$

\

$\"\"$

\

Take natural logarithm on each side.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ years.

\

Therefore, the amount is doubled in $\"\"$ years.

\

$\"\"$

\

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

\

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