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Math Help - Compound interest formula

  1. #1
    Senior Member Mukilab's Avatar
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    Compound interest formula

    Fred invests an amount of money in an account by paying r% compound interest per annum. The amount of money doubles after n years.

    I'm aware of the compound interest formula A=P(1+r/100)^n however I have no idea how to change it according to n.
    Would I start off along the lines of 2A=p(1+r/100)^n?
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  2. #2
    MHF Contributor
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    (1 + r)^n = 2
    n = log(2) / log(1 + r)

    Example: r = .06 (6%)
    n = log(2) / log(1.06) = 11.89566.... ; not quite 12 years
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  3. #3
    Senior Member Mukilab's Avatar
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    Can't use a method that utilises logs
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  4. #4
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    Quote Originally Posted by Mukilab View Post
    Can't use a method that utilises logs
    Well, too bad so sad: that's the only way to solve directly.
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  5. #5
    Senior Member Mukilab's Avatar
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    Its not. I know that for a fact.
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  6. #6
    Senior Member Mukilab's Avatar
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    What about simplifying it so you have the equation pertaining to r
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  7. #7
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    r = 2^(1/n) - 1

    SO?

    IF you know it as a fact: then SHOW US.
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  8. #8
    Senior Member Mukilab's Avatar
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    I know as a fact because it is impossible a question pertaining to logs would show up in a paper that specifies to a certain age that has never previously learned logs and 8 years later they still are not teaching logs to this age group!
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  9. #9
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by Wilmer View Post
    r = 2^(1/n) - 1

    SO?

    IF you know it as a fact: then SHOW US.
    Would it not be

    100(^{n}\sqrt{2}-1)
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  10. #10
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    Quote Originally Posted by Mukilab View Post
    I know as a fact because it is impossible a question pertaining to logs would show up in a paper that specifies to a certain age that has never previously learned logs and 8 years later they still are not teaching logs to this age group!
    Have a good day, Mukilab.
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  11. #11
    Senior Member Mukilab's Avatar
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    Instead of separating Total from investment can I do 2p=p(1+r/100)^n?
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  12. #12
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    Quote Originally Posted by Mukilab View Post
    Instead of separating Total from investment can I do 2p=p(1+r/100)^n?
    That is what Wilmer posted in post 2 (except he cancelled out p which is the next step)

    Quote Originally Posted by Mukilab View Post
    Fred invests an amount of money in an account by paying r% compound interest per annum. The amount of money doubles after n years.

    I'm aware of the compound interest formula A=P(1+r/100)^n however I have no idea how to change it according to n.
    Would I start off along the lines of 2A=p(1+r/100)^n?
    I don't know how you'd solve for n without using logarithms, I doubt it's even possible, perhaps they use logarithms without knowing it?
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