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Compound Interest

  1. Jul 4, 2007 #1
    At what rate of interest compounded quarterly, to the nearest tenth of a percent, will an investment of $1000 grow to $1500 in 5 years?

    I set the problem up 1500=1000(1+x/4)^(4*5)

    I then divided by 1000

    1.5 = (1+x/4)^20

    But this is where I'm stuck.
  2. jcsd
  3. Jul 4, 2007 #2
    Well, that's a twentieth degree polynomial.

    Just take the 20th root of both sides.
  4. Jul 4, 2007 #3


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    Use a logarithm. Get a numerical answer for log(1+x/4). Then exponentiate.
  5. Jul 4, 2007 #4
    Thanks for the replies, I ended up trying that & got

    ln 1.5 = 20 ln (1+x/4)

    ln1.5/20 = ln (1+x/4)

    1+x/4 = e^.02027

    x/4 = .02048

    x = .08191 or 8.2%

    What kept throwing me off was I kept getting the wrong answer because I kept dividing by four. After doing so many of these problems in a row, thought I was getting confused w/what could be done & couldn't be done regarding logarithms. Thanks again for the help.
  6. Jul 4, 2007 #5
    [tex]^{20}\sqrt{1.5}=1+x/4 \mbox{ so that } 4^{20}\sqrt{1.5}-4=x[/tex]

    In fact, that's how you can set up a general formula for nominal interest rates.
    Last edited: Jul 4, 2007
  7. Jul 4, 2007 #6


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    Yes, it's the same thing.
  8. Jul 4, 2007 #7
    Only because you went around and made exp(.02027)=1.5^(1/20) which was an unnecessary step.

    I'm not being adversarial, but the OP should know that there are more tools to use.
    Last edited: Jul 4, 2007
  9. Jul 5, 2007 #8
    Thats pretty interesting, I'm in the logarithm section in pre-calc, so thats why they were used. Good to know that there are other ways to solve the problem as well.
  10. Jul 5, 2007 #9


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    I'm not disagreeing. The method using logarithms simply dates from an age when taking a twentieth root wasn't an easy thing. The logs are one way to accomplish that (by turning the root into division).
  11. Jul 5, 2007 #10
    I just took an actuarial course a couple of semesters ago, and they were able to generate a general formula for variable compounding periods. It utilized mth roots, hence my bias towards them.
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