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November 18th, 2011, 01:39 PM  #1 
Member Joined: Nov 2010 Posts: 53 Thanks: 0  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. 
November 18th, 2011, 01:49 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  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. 
November 19th, 2011, 12:54 AM  #3 
Member Joined: Nov 2010 Posts: 53 Thanks: 0  Re: Urgent! question about differentials
Thanks a lot for your answer, nice and thorough.


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