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Complete the table for a savings account in which interest is compounded continuously.

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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%                            --------                                  ------------

asked Feb 16, 2015 in CALCULUS by anonymous
reshown Feb 16, 2015 by goushi

1 Answer

0 votes

Step 1:

The principal amount image.

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: image.

image

Substitute the value .

Substitute .

years.

Step 2:

The principal amount image.

The rate of interest .

The period of time .

Formula for continuous compounding:.

The total amount is

The total amount after 10 years image.

Solution:

Initial investment Annual rate Time to double Amount after 10 year

image

image

image years image
answered Feb 18, 2015 by Sammi Mentor

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