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Interest a(t) = a(0)(1 + rt)

  1. Jun 17, 2004 #1
    In Mathworld, they define Simple Interest as:

    a(t) = a(0)(1 + rt)

    where a(t) is the sum of principal and interest at time t for a constant interest rate r.

    I just want to know why that 0 is in there. Anything divided by 0 will be 0, thus a(t) = 0?
  2. jcsd
  3. Jun 17, 2004 #2
    I would imagine that a(0) is the principle as it is the sum of the principle and the interest at t=0. Since there is no interest at t=0 the sum of the principle and the interest would be the principle.
  4. Jun 17, 2004 #3
    Anything divided by 0 is undefined...

    They're saying a(t) is a function and a(0) is that function evaluated at t=0.

    It would be more clearly written a[t] = (1 + rt)*a[t=0]

  5. Jun 17, 2004 #4


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    In other words, the "a(0)" is not "a times 0", it is "the function a(t) evaluated at t= 0".
  6. Jun 17, 2004 #5


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    Staff: Mentor

    And in still more words (well, actually less words), "a(0)" is the principal.

    Ironic - I was just looking for this formula so I could buy a car...

    edit: oops - they don't use that formula.
    Last edited: Jun 17, 2004
  7. Jun 17, 2004 #6


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    If you're talking about the depreciation curve, I think that's exponential, not linear.

    Edit : No, you're calculating payments, aren't you. I think that's compounded.
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