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November 18th, 2011, 01:39 PM   #1
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Urgent! question about differentials

Hi, a friend of mine asked me to help him with some math problems, but it has been ages since I did this kind of stuff. Could anyone help me to solve this problem:

Find the time required for a sum of money to double itself at 5% per annum compunded continuosly. Hint. dx/dt = 0.05x, where x is the amount after t years.
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November 18th, 2011, 01:49 PM   #2
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Re: Urgent! question about differentials

Essentially, we need to solve the IVP:

where

The ODE is separable:



Integrate, using initial and final conditions as boundaries:





Now, to find the doubling time we set to get:



Solve for t:



Thus, at 5% annual interest compounded continuously, it takes approximately 13.86 years for the investment to double in value.
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November 19th, 2011, 12:54 AM   #3
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Re: Urgent! question about differentials

Thanks a lot for your answer, nice and thorough.
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