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Thread: 2005 Exam FM Sample Question 17

  1. #1
    Actuary.com - Level I Poster
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    2005 Exam FM Sample Question 17

    To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n=2. Determine i.
    ----

    I know this question has been answered on this website before, but I'm just wondering why my answer isn't right.

    Shouldn't this work...


    98 S(3n,i) + (v^n) 98 S(2n,i) = 8000


    Isn't this considered a deferred annuity since the person is getting the second set of payments from time 2n to 3n??
    The person will receive 98 for all 3n,
    Then after n years, the person will receive 98 more for the next 2n years.
    No?

  2. #2
    Actuary.com - Level II Poster
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    Quote Originally Posted by jshor101 View Post
    To accumulate 8000 at the end of 3n years, deposits of 98 are made at the end of each of the first n years and 196 at the end of the next 2n years. The annual effective rate of interest is i. You are given (1+i)^n=2. Determine i.
    ----

    I know this question has been answered on this website before, but I'm just wondering why my answer isn't right.

    Shouldn't this work...


    98 S(3n,i) + (v^n) 98 (2n,i) = 8000


    Isn't this considered a deferred annuity since the person is getting the second set of payments from time 2n to 3n??
    The person will receive 98 for all 3n,
    Then after n years, the person will receive 98 more for the next 2n years.
    No?

    8000 is accumulated amount.
    So, 98 a(3n,i) + (v^n) 98 a(2n,i) = 8000 (v^3n)
    OR
    98 S(3n,i) + 98 S(2n,i) = 8000

  3. #3
    Actuary.com - Level IV Poster
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    Get rid of the red:

    98 S(3n,i) + (v^n) 98 S(2n,i) = 8000

    Your accumulating, so either bring all the payments back to time 0, and then to time 3n, or take everything to 3n.

  4. #4
    Actuary.com - Level I Poster
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    Thanks- I think I get it...

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