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Thread: Increasing Annuity Immediate

  1. #1
    Actuary.com - Newbie Poster
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    Increasing Annuity Immediate

    Hi, I'm having trouble with this problem. I've done it many times and the answer in my textbook keeps telling me I'm wrong. Then problem is:

    "Max receives $300 in 1 year, $350 in 2 years, $400 in 3 years and so on until the final payment of $800. Using an annual effective rate of interest of 4%, find the present value of these payments at time 0."

    From this question, I know that I have to use the Increasing annuity immediate equation. Which is, (Ia) angle n = (a-double dot-angle n) - (nv^n)/i .
    After calculating all the values, I get that the present value of these payments is $2099.61. The answer that the book has is $4647.00. What am I doing wrong? I've double checked all my values in the (Ia) equation multiple times and I still come up with the same answer.

    Please help. Thank you very much.

  2. #2
    Actuary.com - Level IV Poster
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    Are you breaking the payments up?

    You need to factor out, say, 250a(angle 11)4%. Then you have an increasing annuity left over, 50I(a angle 11)4%, sum those up now.

  3. #3
    Actuary.com - Level III Poster
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    Quote Originally Posted by brandond View Post
    Are you breaking the payments up?

    You need to factor out, say, 250a(angle 11)4%. Then you have an increasing annuity left over, 50I(a angle 11)4%, sum those up now.
    brandond is correct. The formula you are using is the case where the initial payment and the increase value are the same. For instance, your solution would work if you had an original payment amount of 50 one year from now, then 100 two years from now, etc.

  4. #4
    Actuary.com - Level III Poster mathrix's Avatar
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    You need to use the general formula with P=300 (1st term) and Q=50 (increment).

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