Step 1:

The principal amount $\"\"$ $ .

The rate of interest $\"\"$ .

The amount is doubled in $\"\"$

The amount $\"\"$ .

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

$\"\"$

Apply ln on each side.

$\"\"$

Using power rule of logarithms: $\"\"$

$\"\"$

$\"\"$ (since $\"\"$ )

$\"\"$

Substitute $\"\"$ .

$\"\"$

Step 2:

The principal amount $\"\"$ $ .

The rate of interest $\"\"$ .

The period of time $\"\"$ .

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

The total amount is

$\"\"$

The total amount after 10 years $\"\"$ $.

Solution:

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

Initial investment	Annual rate	Time to double	Amount after 10 years
$\"\"$	\ $\"\"$ \	7.75	1834.2