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Math Help - Discounted Promissory note

  1. #1
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    Discounted Promissory note

    Here's the question and please help me..

    A five (5) year promissory note for $1,000, bearing interest at 9% compounded annually, was discounted at 12% compounded semi-annually yielding proceeds of $1,416.56.




    1. What was the amount of the compound discount?

    thanks in advance

    EDIT: Am I suppose to find FV and subtract the proceeds from it?
    Last edited by petedam; July 1st 2010 at 09:12 AM.
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  2. #2
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    Whoever holds that promissory note is guaranteed to receive
    1000(1.09^5) = 1538.62 at the maturity date of the note.

    If someone "bought" that note for 1416.56 and will earn 12% cpd semi-annually,
    then he MUST have bought it a bit before maturity date; in other words, 1416.56
    at this rate for some period of time T accumulates (has future value) of 1538.62

    SO: 1416.56(1.06)^T = 1538.62
    Solving for T gives ~1.4185... or 1.42 (rounded) semi-annual periods.

    1.42 semi-annual periods = 8.5 months (rounded).
    So purchase made after 4 years and 3.5 months: 4.29 years

    1000(1.09)^4.29 = 1447.30 ; so:
    1447.30 - 1416.56 = 30.74 ... which is the discount amount.

    Above by Wilmer, discounter extraordinaire
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  3. #3
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    Thank you very much!
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  4. #4
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    Quote Originally Posted by Wilmer View Post
    Whoever holds that promissory note is guaranteed to receive
    1000(1.09^5) = 1538.62 at the maturity date of the note.

    If someone "bought" that note for 1416.56 and will earn 12% cpd semi-annually,
    then he MUST have bought it a bit before maturity date; in other words, 1416.56
    at this rate for some period of time T accumulates (has future value) of 1538.62

    SO: 1416.56(1.06)^T = 1538.62
    Solving for T gives ~1.4185... or 1.42 (rounded) semi-annual periods.

    1.42 semi-annual periods = 8.5 months (rounded).
    So purchase made after 4 years and 3.5 months: 4.29 years

    1000(1.09)^4.29 = 1447.30 ; so:
    1447.30 - 1416.56 = 30.74 ... which is the discount amount.

    Above by Wilmer, discounter extraordinaire
    Just letting you know..the answer should be as follow as told by my instructor

    i = j/m = 9%/1 = 9%
    n = 5
    FV = PV(1 + i)n
    = $1,000(1 + .09)5
    = $1,538.62
    Compound discount = $1,538.62 - $1,416.56 = $122.06
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  5. #5
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    Quote Originally Posted by petedam View Post
    Just letting you know..the answer should be as follow as told by my instructor
    i = j/m = 9%/1 = 9%
    n = 5
    FV = PV(1 + i)n
    = $1,000(1 + .09)5
    = $1,538.62
    Compound discount = $1,538.62 - $1,416.56 = $122.06
    Ok then, could you ask that instructor of yours to define "compound discount".
    IF what you posted is correct, he HAS to tell you:
    "compound discount means the future value of the original note less the proceeds from selling the note"

    ...which is really silly, and really means "nothing", except a simple future value calculation.
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  6. #6
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    "compound discount means the future value of the original note less the proceeds from selling the note"

    A five (5) year promissory note for $1,000, bearing interest at 9% compounded annually, was discounted at 12% compounded semi-annually yielding proceeds of $1,416.56.


    yes that's what she did...she figured out the FV and subtracted the proceeds from selling the note.
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  7. #7
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    Quote Originally Posted by petedam View Post
    yes that's what she did...she figured out the FV and subtracted the proceeds from selling the note.
    Ya...so the problem boils down to a simple subtraction of really 2 given amounts:

    GIVEN: A five (5) year promissory note for $1,000, bearing interest at 9% compounded annually, ...
    That's 1538.62
    GIVEN: was discounted at 12% compounded semi-annually yielding proceeds of $1,416.56.
    That's 1416.56

    1538.62 - 1416.56 = 122.06

    I see no real "purpose" here...
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  8. #8
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    Quote Originally Posted by Wilmer View Post
    Ya...so the problem boils down to a simple subtraction of really 2 given amounts:

    GIVEN: A five (5) year promissory note for $1,000, bearing interest at 9% compounded annually, ...
    That's 1538.62
    GIVEN: was discounted at 12% compounded semi-annually yielding proceeds of $1,416.56.
    That's 1416.56

    1538.62 - 1416.56 = 122.06

    I see no real "purpose" here...
    The purpose is to trick you and it did tricked me. Originally that's what i thought i had to do. Have a look at my original question.

    "EDIT: Am I suppose to find FV and subtract the proceeds from it? "
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  9. #9
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    Quote Originally Posted by petedam View Post
    "EDIT: Am I suppose to find FV and subtract the proceeds from it? "
    Dunno. I give up! Ask that "instructor?" of yours!
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  10. #10
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    Quote Originally Posted by Wilmer View Post
    Dunno. I give up! Ask that "instructor?" of yours!
    No I am not asking you any more question the quote in red was part of my original post. which turns out to be the way it should have been calculated "according" to my instructor.
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