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Rainbow Annuity

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  • Rainbow Annuity

    I've got a rainbow annuity like so:

    pmt: 1 2 3 .... n n n-1 .... 2 1
    time: 1 2 3 .... n n+1 n+2 ...2n-1 2n

    I need to compute the present value at time t = 1. My book does it by breaking it up into a bunch of value-1 annuities and then adding them up (ie, time 1 to 2n, 2 to 2n-1, etc).

    *i* want to do it by treating it as two annuities, finding the present value of them, and combining them.

    IE: first annuity is just an increasing annuity from time 1 to n, second annuity is just a decreasing annuity from time n+1 to 2n.

    HOWEVER I cannot get this to turn into the answer from the book - i'm not sure how to type these symbols into the computer either .. but take my word, I think my problem is how to 'discount' the second annuity properly to find it's present value at time 1.

    Thoughts?

  • #2
    the decreasing annuity formula will give you the present value of the decreasing annutiy at time n. You need to discount the entire result back to time 0 and then add the pv of the increasing annuity. I think it should be (Ia)angle n + [v^n *(Da)angle n]. Someone correct me if im wrong.

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    • #3
      Originally posted by PhillyP
      the decreasing annuity formula will give you the present value of the decreasing annutiy at time n. You need to discount the entire result back to time 0 and then add the pv of the increasing annuity. I think it should be (Ia)angle n + [v^n *(Da)angle n]. Someone correct me if im wrong.
      That sounds right.

      But I did like the way they set up that rainbow annuity - n annuities, each starting at times 1, 2 ... n.

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      • #4
        Originally posted by wat
        That sounds right.

        But I did like the way they set up that rainbow annuity - n annuities, each starting at times 1, 2 ... n.
        I like it too - now that I've seen it - but I never would have come up with it on my own, and I worry about being able to come up with similar things on an exam.

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        • #5
          spam - banned
          Last edited by Irish Blues; October 5 2010, 08:19 AM.

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          • #6
            (PMT * Ia n,i + v^n * PMT * Da n,i) * (1+i) should give you the correct answer

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            • #7
              This thread is 4 years old. A spam bot bumped it.

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              • #8
                nice, well at least i can pad my post count a little bit well I'm at it

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