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Math Help - logarithmic word problem

  1. #1
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    logarithmic word problem

    Hello, here is my problem:

    Alex invests $50,000 at an interest rate of 0.7% compounded monthly. Laura invests $40,000 at 9.5% compounded annually. After how many years will the two investments be equal in value?

    okay so this is what I have so far

    50,000 x (.07x12)^n=x

    40,000 x .095^n=x

    I am not really sure how to set up the equation and I'm pretty sure I started off wrong, help is much appreciated!

    Thank you!
    Dan
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  2. #2
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    Re: logarithmic word problem

    The 1st amount gets multiplied by 1.007 each month and the 2nd amount by 1.095 each year.
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  3. #3
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    Re: logarithmic word problem

    it should have been: 50,000 x (1.07^n)12=x and 40,000 x (1.095 ^n)=x I think im figuring it out. Biffboy, i think you ment to write 1.07
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  4. #4
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    Re: logarithmic word problem

    If the interest rate is 0.7% we multiply by 1.007. If you meant 7% we multiply by 1.07. In your question you said 0.7%
    Also n years =12n months so with the 50000 the index will be 12n
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  5. #5
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    Re: logarithmic word problem

    The reason i cant figure it out is because it has two variables. In the answers n= 10.6, but if you sub that in the x variable in each equation are different when they should be the same according to the question in the first post. I am clearly missing something...
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  6. #6
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    Re: logarithmic word problem

    The first rate can't be 7% per month as amounts then would never be equal. So it must be 0.7% and you should be multiplying by 1.007^(12n)
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  7. #7
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    Re: logarithmic word problem

    I made a mistake writing the problem, sorry it is 7% not 0.7%, and 9.5%. My bad... Thank you for you help though, I'm busting out the calculator right now!
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  8. #8
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    Re: logarithmic word problem

    Quote Originally Posted by Dwahl View Post
    Hello, here is my problem:

    Alex invests $50,000 at an interest rate of 0.7% compounded monthly. Laura invests $40,000 at 9.5% compounded annually. After how many years will the two investments be equal in value?

    okay so this is what I have so far

    50,000 x (.07x12)^n=x
    No "7% compounded monthly" does NOT mean 7% per month. It is still 7% per year which is .07/12= 0.00583 percent per month. In n years, there are, of course, 12n months so it will be 50000(1.00583)^{12n}

    40,000 x .095^n=x
    And this should have been 40000(1.095)^n
    Set them equal and solve for n.

    I am not really sure how to set up the equation and I'm pretty sure I started off wrong, help is much appreciated!

    Thank you!
    Dan
    Thanks from Dwahl
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  9. #9
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    Re: logarithmic word problem

    this is what i have so far, thanks for all your help guys, I really appreciate it!

    50000 (1.00583)^12n = 40000 (1.095)^n

    log(50000 x 1.00583^12n) = log(40000 x1.095^n)

    log 50000 + log 1.00583^12n = log 40000 + log 1.095^n

    log 50000 + 12n log 1.00583= log 40000+ n log 1.095

    and this is sort of where i get a bit lost, below is what i did.

    log 50000 - log 40000= -12n log 1.00583 + n log 1.095

    Im not sure how to simplify it anymore. so i tried this

    __ log 50000- log 40000____ = n+n
    -12 + log 1.00583 + log 1.095

    Can I get a little more help simplifying it, because I know I did it wrong :/ thanks again!
    Last edited by Dwahl; May 1st 2012 at 09:30 PM.
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  10. #10
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    Re: logarithmic word problem

    Last line wrong. In the previous line write the right hand side as n(log1.095-12log1.00583)
    Thanks from Dwahl
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