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Math Help - Continuous Compound Interest problem

  1. #1
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    Continuous Compound Interest problem

    So I know this is the formula,
    A
    = Pe rt

    To what final amount will an initial investment of $5,000 grow if the interest rate is 4% per year compounded continuously for 21 years? Write your answer rounded to the nearest cent.


    im getting a number of 7.994 but it doesnt seem right.
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  2. #2
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    Quote Originally Posted by av8or91 View Post
    So I know this is the formula,
    A
    = Pe rt

    To what final amount will an initial investment of $5,000 grow if the interest rate is 4% per year compounded continuously for 21 years? Write your answer rounded to the nearest cent.


    im getting a number of 7.994 but it doesnt seem right.
    Of course it's not right as $5000 > 7.994 and the problem implies that the amount increases

    P = 5000e^{21 \times 0.04} = \$11,581.83
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  3. #3
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    I dont understand what im doing wrong. 5000e^(.04)(21) Then where do I proceed. P=.84ln5000e?
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  4. #4
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    Quote Originally Posted by av8or91 View Post
    I dont understand what im doing wrong.
    You're doing nothing wrong,

    evaluate this!

    Quote Originally Posted by av8or91 View Post
    5000e^(.04)(21)
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  5. #5
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    Maybe thats my issue, im just evaluating it wrong. .84ln5000e does the equal .84ln13590? Then what I am doing is taking the natural log of 13590 mulitply by .84 but no thats not right.
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  6. #6
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    Quote Originally Posted by av8or91 View Post
    Maybe thats my issue, im just evaluating it wrong. .84ln5000e does the equal .84ln13590? Then what I am doing is taking the natural log of 13590 mulitply by .84 but no thats not right.
    You don't need to use the natural log at all.

    You're trying to find A given P, r and t. You can directly substitute the given values into the equation you gave in the OP to find a value for A
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  7. #7
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    Maybe im a little stupid but thats why im here for help, . Can you please show me how you are not using any natural logs and how you did it. Much appreciated.
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  8. #8
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    There are no logs in your original equation therefore consider

    A = Pe^{rt}

    inputing the information given

    A= 5000e^{0.04\times 21}

    A = 5000e^{0.84}

    A = 5000\times 2.316

    A = 11,581.83

    that is all.
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  9. #9
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    Ok Thanks. I see that now but when would you use ln
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  10. #10
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    Quote Originally Posted by av8or91 View Post
    Ok Thanks. I see that now but when would you use ln
    In the problem you provided!?!
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  11. #11
    DBA
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    In this problem you have all variables given (P, r and t)

    In this example you would use ln:

    How long will it take to double your investment if the interest would be 6% compounded continuousely?

    A= P * e^rt

    P = 1000
    A = 2000
    r = 0.06

    2000 = 1000 * e^0.06*t
    2 = e^0.06*t
    ln2 = ln e^0.06*t --> ln e^x = x
    ln2 = 0.06*t
    t= ln2/0.06
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