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Math Help - Present Values

  1. #1
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    Present Values

    Find present value as at january 2009 of a series of payments of 100 payable on first day of each month during years 2010,2011,2012. Assume effective rate of interestof 8% p.a
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  2. #2
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    Quote Originally Posted by mukrosa View Post
    Find present value as at january 2009 of a series of payments of 100 payable on first day of each month during years 2010,2011,2012. Assume effective rate of interestof 8% p.a
    Why is that funny? Would it be less or more funny if it were 7%?

    You MUST learn "Basic Principles".

    Define i_{annual effective} = 0.08

    Define i_{monthly effective} = 1.08^{1/12}-1

    Define v = v_{monthly} = \frac{1}{1+i_{monthly effective}}

    The first payment is one year away from the valuation date.

    100(v^{12} + v^{13} + ... + v^{47})

    Can you add them up?
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  3. #3
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    Not Sure

    The payments were being made daily so mayb we ought to use[iΛ(364)][/]wat do u tnk?
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  4. #4
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    Please get your problem CLEAR, then post it again

    To see where you're at, can you answer this:
    what is the present value of a series of 12 monthly payments,
    starting in 1 month from now, at 12% annual compounded monthly?
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  5. #5
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    Often a monthly approximation is sufficient for payments made on the same day of each month.

    Please be clear about the use fo the word "effective". Make sure you mean it.
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  6. #6
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    the monthly effective rate=0.11386 then i assume value of payments is 1 [(1-vΛn)/i=(1-(1/1.11386)Λ12)/0.11386=6.37469][/MATH
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  7. #7
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    Quote Originally Posted by mukrosa View Post
    the monthly effective rate=0.11386 then i assume value of payments is 1 [(1-vΛn)/i=(1-(1/1.11386)Λ12)/0.11386=6.37469][/MATH
    NO. "12% annual compounded monthly" means 1% per month, so 1.01^12 - 1 = .126825 (12.6825% effective).

    You assumed "12% effective annual compounded monthly", or:
    (1 + i)^12 = 1.12 ; i = .009488... ; i * 12 = .11386...

    Even at that, you need to use .009488 in your calculation, not .11386:
    [1 - (1 / 1.009488)^12] / .009488 = 11.2915...

    So, using $100 per month, present value is $1129.15

    Your original problem states: "Assume effective rate of interestof 8% p.a".
    The word "effective" means (1 + i)^12 = 1.08.
    If instead it was: "Assume rate of interestof 8% p.a compounded monthly", then:
    effective annual rate = (1 + .08/12)^12 - 1 = .0829995... (~8.3%)
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