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the problem is:

Find the time required for money invested at an annual rate of 4% to double in value if the investment is compounded continuously. Round to the nearest hundredth of a year.

please help
 Dec 9, 2013
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mathmathmath:

the problem is:

Find the time required for money invested at an annual rate of 4% to double in value if the investment is compounded continuously. Round to the nearest hundredth of a year.

please help



You have to give the initial amount of money a value. It doesn't matter how much because $5 will double in the same amount of time as $1000 will double.
I'm going to start with $1 because it is easiest and I need to work out how long it will be before I have $2.

Inially I have $1
After one year I have $1*1.04 = 1.04 (dollars)
After 2 years I have 1.04*1.04 = 1.04 2
After 3 years I have 1.04 2*1.04 = 1.04 3

After n years I have 1.04 n dollars
The answer will be given by the equation

2=1.04 n
Since it is the exponent that you need to find, you wil need to take the log of both sides to get the answer.

Try to finish it by yourself.
 Dec 10, 2013

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