Question

Complete the table for a savings account in which interest is compounded continuously.
Initial                       Annual             Time to                      Amount After
Investment              % Rate             Double                        10 Years

$750                          -                      73/4yr                                -

Answer 1

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