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Thread: Help with Bonds

  1. #1
    Junior Member
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    Feb 2012
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    Help with Bonds

    What is the purchase price of a bond that is issued on May 1,2002 for 22 years at a coupon
    rate of 9.4% compounded semi-annually? The maturity date of the bond is May 11,2007 and the yield
    rate is 8.5% compounded semi-annually. The bond has a face value of $5000 and it is redeemable
    at par.
    I have FV= 5000 PMT= 235 i=.0425 n=5.5

    5000(1.0425^-5.5) + 235(1-1.0425^-5.5)/.0425
    5000(.795393) + 235(4.814282)
    3976.965000 + 1131.356353 = 5108.321353
    The answer is not correct could someone help me find out where I went wrong?

  2. #2
    Elite Member
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    Let's see... 2007 - 2002 = 5 -- Nope! That is NOT 22 years.

    If this is one bond, I wonder if we can make sense of what you have written...

    Pmt = 5000*0.094/2 = 235.00 -- Good.

    Yield is 8.5%, so semi-annual yeild is 4.25% Define i = 0.0425 and v = 1/1.0425 and we have PV coupons: Pmt*(v-v^45)/(1-v) = Pmt*(1-v^44)/i = 235*19.76008 = 4643.619
    Add this to 5000*v^44 = 800.983
    And we have a purchase price: 4643.619 + 800.983 = 5444.60

    The value on May 1, 2002, given the maturity at May 11, 2007. That's two pieces.

    The value on May 11, 2002 is Pmt*(1 + v + ... + v^10) = Pmt*(1-v^11)/(1-v) = Pmt*(1-v^11)/(i*v) = Pmt*(1-v^11)/d
    Increased by 5000v^11

    Two things left for you to do. Calculate these values and then tell me why I cared about 5/11/2002 instead of 5/1/2002.

  3. #3
    Junior Member
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    Feb 2012
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    Reply to Bond question

    I believe you cared about 5/11/02 because it is when the bond is maturing.
    V=1/1.0425
    235(1+.959233+X+.959233^10=235(1-.959233^11)/1-.959233=235(1-.959233^11)/1-.959233=235(1-.959233^11)/d
    235(1.959233+X+.659519=235(.367348/.04767)=235(7.706063)=235(1-.367348/.04767)/d
    235(2.618752X)+
    615.406720X=1810.924691=235(.367348)/d
    615.406720X=1810.924691=86.326780/d
    .339830X=86.326780/d
    Okay this is as far as I get.
    The teacher said today we don't use 22years after 1st part of question
    She also gave us 5 possible answers which are a)$5413.30 b)$5431.30 c)4531.30 d)4533.30 e)$4513.30
    I'm really not understanding this question.....I have final exam on Tuesday and my lil brain is not computing.

  4. #4
    Junior Member
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    That is the exact question

    Hello
    This is the exact question taken word for word from the assignment sheet as given to our class.

  5. #5
    Junior Member
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    Feb 2012
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    Help Please!

    First, I ignore the 22 year part. It has no bearing since the maturity date is May 11, 2007.

    Because the purchase date is before the maturity date in the calendar year, I took the bond back to Dec. 11, 2001 (basically made n -11 instead of -10). So I calculated both the FV and the PMT totals using 11 periods (Dec. 11, 2001 to May 11, 2007) which gave me the bond value on Dec. 11, 2001.
    Lastly, I added in the simple interest from Dec. 11, 2001 to the purchase date of May 1st, 2002 which gave me the value on May 1st, 2002.
    but still not getting the right answer.

  6. #6
    Elite Member
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    May 11/02 : 5year bond purchased; maturity May 11/07;
    face $5000, coupons $235, rate 4.25 s/a: PV = 5180.24

    BUT purchase made 10 days earlier: May 1/02;
    10 days later, a coupon amount of $235 is received:
    you gotta PAY for that: 5180.24 + 235 = 5415.24 :
    but not quite: you should get a "little discount!" since
    you wait 10 days...that's apparently $1.94; sooooo:
    5415.24 - 1.94 = 5413.30 (your choice a).

    That's my take on this messy problem....
    I'm just an imagination of your figment !

  7. #7
    Junior Member
    Join Date
    Feb 2012
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    114

    Thanks Denis

    My mistake was in the in 5 year bond purchase I had 5.5years
    This is a very badly worded problem, Messy just about covers it.
    Thanks Dennis for taking the time to help out. Makes sense to me now.

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