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Thread: Force of interest problem

  1. #11
    Actuary.com - Level I Poster
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    Quote Originally Posted by Kenneth View Post
    Nope. Did you take the natural log first? The interest rate is increasing over time, not decreasing.

    I get m = .01 and b = .07

    It's easy to drop a step in force of interest problems. You'll often get an answer that isn't obviously wrong. That answer is also sometimes one of the other multiple-choice answers.

    I must be forgetting basic maths or something because when i get to here:

    ln(1.03691504) = .125 m + .5 b
    ln(1.05687083) = .28125 m + .75 b


    0.03624999725 = .125 m + .5 b
    0.05531249507 = .28125 m + .75b

    and when i solve for the values of b & m I end up with them ridiculous long decimal numbers as opposed to 0.1 & 0.7

  2. #12
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    Quote Originally Posted by Ronan1990 View Post
    I must be forgetting basic maths or something because when i get to here:

    ln(1.03691504) = .125 m + .5 b
    ln(1.05687083) = .28125 m + .75 b


    0.03624999725 = .125 m + .5 b
    0.05531249507 = .28125 m + .75b

    and when i solve for the values of b & m I end up with them ridiculous long decimal numbers as opposed to 0.1 & 0.7
    Show me your steps.

  3. #13
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    Quote Originally Posted by Kenneth View Post
    Show me your steps.
    0.125m + 0.5b = 0.03624999725 (ln(1.03691504))
    0.28125m + 0.75b = 0.05531249507

    so simultaneous equations, multiply the top line by -1.5 to get

    -0.1875m -0.75b = -0.05437499588
    0.28125m +0.75b = 0.05531249507

    which cancels to some really long decimal value for m so I must be doing my simultaneous equations wrong

  4. #14
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    Quote Originally Posted by Ronan1990 View Post
    0.125m + 0.5b = 0.03624999725 (ln(1.03691504))
    0.28125m + 0.75b = 0.05531249507

    so simultaneous equations, multiply the top line by -1.5 to get

    -0.1875m -0.75b = -0.05437499588
    0.28125m +0.75b = 0.05531249507

    which cancels to some really long decimal value for m so I must be doing my simultaneous equations wrong
    -0.1875m -0.75b = -0.05437499588
    0.28125m +0.75b = 0.05531249507

    adding them up:

    .09375m = .00093749919

    dividing by the whole number in front of the m (including the sign), I get:

    m = .00999999136

    I feel safe in rounding this to .01

    When I ask for steps, I'm not asking for step 1 of 6, I'm asking for all 6 steps.

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