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deferred perpetuity immediate problem

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  • deferred perpetuity immediate problem

    I am still having a hard time with deferred perpetuities.

    Here is my problem:

    A deferred perpetuity-immediate paying $2000 monthly is bought for a sum of $229,433.67. Find the deferred period if i = .06

    My book mentions deferred annuities but not deferred perpetuities, I assume the concept is similar in both cases though.

    This is what I was thinking of doing:

    229433.67 = 2000*v^m*a(infinity, .06)

    where a(infinity, .06) is a perpetuity immediate taken at 6%

    so I solve for m and I end up getting -33.10609 which cant be right since it is obviously not a negative period of time.

    What am I doing wrong? Any help is appreciated

  • #2
    I think you have the same issue here as in the other question you posted. You need to make sure if the interest rate in the question is quoted as an annual rate or something else.

    Also, algebraically solve for your a(infinity) for both perpetuities-immediate and perpetuities-due. You'll find that the formula for each is very simple.

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    • #3
      I would also guess that they are quoting nominal rates which I am not sure you are using.
      Whether you are the lion or the gazelle, when the sun comes up, you better be running.

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