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Thread: Perpetuity due question

  1. #1
    Actuary.com - Newbie Poster
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    Perpetuity due question

    Question from Nov/97 #2

    I have a question about the first part of the question.

    "Present value of the perpetuity if $9.25. The perpetuity pays $1 at the end of every 2 years with the first payment immediately...."

    In the solution manual this is given for the first part of the question:

    Let j = effective rate for a 2-year period. Then PV of the perpetuity due =

    1 + 1/j = 9.25, j = 1 / 8.25 = .1212

    My question is, how do you setup the equation above without consdiering the discount rate. I can't seem to figure it out. Thanks.

  2. #2
    Actuary.com - Level VI Poster Ken's Avatar
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    If you compare the streams of payments, a perpetuity due is a perpetuity immediate plus a payment at time zero so a perpetuity due = 1 + 1/i
    Whether you are the lion or the gazelle, when the sun comes up, you better be running.

  3. #3
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    The discount rate, d = i/(1+i)

    The PV of the perp = 1/d = 1/(i/(1+i))

    Flip it around and it becomes = 1 + 1/i must easier than working with d.

  4. #4
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    Thanks for the feedback. I get it now. I was also looking at definitions of i and d and I saw an equation I forgot about.

    1 = 1/d - 1/i

    Which is basically what you guys have said. Thanks again.

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