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February 10th, 2018, 11:01 AM   #1
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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 12:27 PM.
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February 10th, 2018, 01:06 PM   #2
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after n months:

account A 2000(1+.0225/12)^n
account B 2000(1+.03/12)^n

Find n when sum exceeds 5000.
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February 10th, 2018, 01:48 PM   #3
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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
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February 12th, 2018, 07:08 AM   #4
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Mathman, Denis, Thank you!
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February 12th, 2018, 07:32 AM   #5
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I got you 5001 instead of 5000: you owe me a dollar!!
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