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Dr. Finan FM/2 - Problem 4.9(Simple interest rate)

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  • Dr. Finan FM/2 - Problem 4.9(Simple interest rate)

    Problem 4.9
    Suppose that the accumulation function for an account is a(t) = 1 + 3it

    At time 0, you invest $100 in this account.

    If the value in the account at time 10 is $420, what is i?

    -------------------------------------------------------------------------------------

    The solutions manual says 10.66%, however, I got 14% after doing it a couple of more times.

    PV = 100
    FV = 420
    a(0) = 1
    a(10) = 1 + 30i

    420 = 100 * (1 + 30i - 1 / 1 )

    i = 14% from here. However, while I'm sure it's 14%, I'm not 100% sure. If it's 10.66% as the solutions say, could someone point this out? Thanks!

  • #2
    The equation you set up is wrong.

    Let me rearrange your equation:
    420/100 = (1 + 30i -1 / 1 )

    LHS = the final value / initial value
    RHS = (the final value - initial value / initial value)
    I think you may want your RHS to be (1 + 30i -1 ) / 1 which is (the final value - initial value ) / initial value

    Anyway, LHS <> RHS.

    Now, I think you know what's wrong with your equation.

    Comment


    • #3
      I didn't understand BeanCounter's explanation, so I set it up the way I learned it.
      100a(10) = 420
      100[1+3i(10)] = 420

      Comment

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