SOLUTION: How many months will it take until an account will have $3,500 if $2,500 is invested now at 5% compounded monthly?

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Question 207524: How many months will it take until an account will have $3,500 if $2,500 is invested
now at 5% compounded monthly?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
5% compounded monthly = .05/12 = .00417
present value = 2500
future value = 3500
formula is 2500+%2A+%281.00417%29%5Ex+=+3500
you can solve this with logarithms.
you get log%28%282500%2A1.00417%29%5Ex%29%29+=+log%28%283500%29%29
by the laws of logarithms, this becomes:
log%28%282500%29%29+%2B+x%2Alog%28%281.00417%29%29+=+log%28%283500%29%29
finding the logs on your calculator make the equation equal to:
3.397940009 + .001807243*x = 3.544068044
solving for x, you get:
x = 80.85690519 months
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to prove this is true, substitute in the original equation of 2500+%2A+%281.00417%29%5Ex+=+3500 to get 3500.
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your answer is:
x+=+80.85690518
1.00417%5Ex+=+1.4
1.4+%2A+2500+=+3500
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