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

$ 4000                                6%                            --------                                  ------------

Answer 1

Step 1:

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.

Using power rule of logarithms: .

Substitute the value .

Substitute .

years.

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 year
		years