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Math Help - Annuity: Present Value

  1. #1
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    Annuity: Present Value

    I have absolutely no idea what I am doing. I study with OTEN (I work from home), so asking a teacher becomes a problem.

    Here's the question:
    A relative wills you an annuity paying $7400 per half-year for the next 10 years. If this money can earn 6.5% pa compounded half-yearly, what is the present value of this annuity?

    I've been through numerous answers, but when I re-work through the answer it does not seem to add up. They seem to be unreasonably too high or too low. Right now, this is what I come up with:

    r=0.065 / 2 = 0.033
    N=M(1+r)^n-1 / r(1+r)^n
    N=7400 (1+0.033)^20 1 / 0.033(1+0.033)^20
    =7400(1.033^20-1) / (0.033x1.033^20)
    =$107,100.80


    That's based off similar example questions. That seems incredibly wrong. The previous way I did it, I skipped the second last line, and the answer seemed too high - this one seems too low!


    Like I said, I'm basing all that on example questions. So I don't know why it looks so wrong.


    Can you tell me what I'm doing wrong, and give me the right way to do it.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by F4LL3N View Post
    A relative wills you an annuity paying $7400 per half-year for the next 10 years. If this money can earn 6.5% pa compounded half-yearly, what is the present value of this annuity?

    r=0.065 / 2 = 0.033
    N=M(1+r)^n-1 / r(1+r)^n
    N=7400 (1+0.033)^20 1 / 0.033(1+0.033)^20
    =7400(1.033^20-1) / (0.033x1.033^20)
    =$107,100.80
    Answer is 107,591.16
    Change your "r" to .065 / 2 =.0325 (very important)
    So you basically are doing it right.

    EASIER like this:
    P = Present value ( ?)
    a = annuity amount (7400)
    n = number of periods (20)
    i = periodic interest rate (.0325)
    Formula:
    P = a[1 - 1/(1 + i)^n] / i

    P = 7400[1 - 1/(1+.0325)^20] / .0325 = 107591.16
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  3. #3
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    Oh, okay. Thanks. So it was only the rate I got wrong.

    I thought my answer would have been 60,000 too low atleast. I guess I don't really understand it all yet.
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