$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

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

\

The amount $\"\"$ .

\

Compounded continuously.

\

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

\

$\"\"$

\

$\"\"$

\

Apply ln on each side.

\

$\"\"$

\

Apply power rule of logarithms : $\"\"$ .

\

$\"\"$

\

Substitute the value of $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$ years.

\

$\"\"$

\

The principal amount $\"\"$ .

\

The rate of interest $\"\"$ .

\

The period of time $\"\"$ .

\

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

\

The total amount is,

\

$\"\"$

\

The total amount after $\"\"$ years $\"\"$ $.

\

$\"\"$

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Initial investment	Annual rate	Time to double	Amount after $\"\"$ years
$\"\"$	\ $\"\"$ \	$\"\"$	$\"\"$

\