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Math Help - Compound interest

  1. #1
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    Compound interest

    I have this log question,

    How long will it take an intiatial investment to grow by 50 % in each of the following cases:

    A) 5% per year, i wont write b, c because they are more or less the same.

    my problem is i dont know how to set up the problem this is what i see

    Initial amount= ?
    final amount?
    growth rate= 1.05 (1+.5)
    T=?
    95%=A(1.05%)^t

    I do not know how to incorporate the rate at which it compounds nor do i know how to add the 5%

    Can i just assume A?.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Compound interest

    If the investment has grown by 50%, then the amount A the investment is worth is A=1.5P where P is the principal. Compounded annually at an interest rate of r, we would write:

    1.5P=P(1+r)^t

    Now, divide through by P to get:

    1.5=(1+r)^t

    Now you can use logs to solve for t.
    Thanks from Gurp925
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  3. #3
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    Re: Compound interest

    If it is coumpounded anually would it be T/12 or for instance of it ask compounded quarterly T/4?
    Quote Originally Posted by MarkFL View Post
    If the investment has grown by 50%, then the amount A the investment is worth is A=1.5P where P is the principal. Compounded annually at an interest rate of r, we would write:

    1.5P=P(1+r)^t

    Now, divide through by P to get:

    1.5=(1+r)^t

    Now you can use logs to solve for t.
    Last edited by Gurp925; May 12th 2013 at 01:13 PM.
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  4. #4
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    Re: Compound interest

    Since r is interest per year, t will be in years

    The answer should be 8.31 years. If you got 5% compounded monthly from a bank then the answer would be 8.31 months to increase your investment by 50%
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Compound interest

    Quote Originally Posted by Gurp925 View Post
    If it is compounded annually would it be T/12 or for instance of it ask compounded quarterly T/4?
    A more general formula is:

    A=P\left(1+\frac{r}{n} \right)^{nt}

    where n is the number of times the interest is compounded annually.
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  6. #6
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    Re: Compound interest

    great
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