February 10th, 2018, 12:01 PM  #1 
Newbie Joined: Jul 2015 From: NEW YORK Posts: 10 Thanks: 0  Word problem
You deposit \$2000 in account A, which pays 2.25% annual interest compounded monthly. You deposit another \$2000 in Account B, which pays 3% annual interest compounded monthly. When is the sum of the balance in both accounts at least \$5000? Thank you in advance! Last edited by greg1313; February 10th, 2018 at 01:27 PM. 
February 10th, 2018, 02:06 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,436 Thanks: 562 
after n months: account A 2000(1+.0225/12)^n account B 2000(1+.03/12)^n Find n when sum exceeds 5000. 
February 10th, 2018, 02:48 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,658 Thanks: 740 
u = (1 + .0225/12) v = (1 + .03/12) 2000(u^n) + 2000(v^n) = 5000 ; divide by 2000: u^n + v^n = 5/2 Brute solving: after 102 months: A = ~2421, B = ~2580, A + B = 5001 
February 12th, 2018, 08:08 AM  #4 
Newbie Joined: Jul 2015 From: NEW YORK Posts: 10 Thanks: 0 
Mathman, Denis, Thank you! 
February 12th, 2018, 08:32 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,658 Thanks: 740 
I got you 5001 instead of 5000: you owe me a dollar!!


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