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Math Help - Calculate the Price of a Bond

  1. #1
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    Calculate the Price of a Bond

    2. (a) Find the price of the bonds or debentures given V = 100 and r, i, and n as stated.

    (i) 20 years to maturity, interest at 10% p.a. to yield 11% p.a.

    My attempt at a solution is as follows:

     P = V(1 + i)^{-n} + rV\frac{1 - (\frac{1}{1 + i})^n}{i}

     = V(1 + 0.11)^{-20} + 0.10*100\frac{1 - (\frac{1}{1 + 0.11})^{20}}{0.11}

    = \$92.04.

    Though apparently I'm wrong since the correct answer is listed as \$91.98. Why am I getting a different answer? Almost none of my answers are the same as those on the answer page, as I am always off by quite a few cents. The only thing I can think of is that the values given above aren't actually the values supposed to be subbed in, and that I need to perform some other calculations in order to get such values.
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  2. #2
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    Re: Calculate the Price of a Bond

    Nvm, I got it.
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  3. #3
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    Re: Calculate the Price of a Bond

    Quote Originally Posted by RogueDemon View Post
    2. (a) Find the price of the bonds or debentures given V = 100 and r, i, and n as stated.

    (i) 20 years to maturity, interest at 10% p.a. to yield 11% p.a.

    My attempt at a solution is as follows:

     P = V(1 + i)^{-n} + rV\frac{1 - (\frac{1}{1 + i})^n}{i}

     = V(1 + 0.11)^{-20} + 0.10*100\frac{1 - (\frac{1}{1 + 0.11})^{20}}{0.11}

    = \$92.04.

    Though apparently I'm wrong since the correct answer is listed as \$91.98. Why am I getting a different answer? Almost none of my answers are the same as those on the answer page, as I am always off by quite a few cents. The only thing I can think of is that the values given above aren't actually the values supposed to be subbed in, and that I need to perform some other calculations in order to get such values.
    Just to write so others reading the post can see why there were two prices for the same par value bond. It has to do with the number of payments the bond makes. When the bond pays semi annual interest payment the price of the bond is $91.98 and when the bond makes an annual interest payment the price of the bond is $92.04

    Compounding = semi annually
    Par Value = 100
    Coupon Rate = 0.05
    Market Rate = 0.055
    N = 40

    Non Zero Bond Price Formula

    Coupon Rate x Par Value x PVIFA(ytm%, n) + Par Value x PVIF(ytm%, n)

    PVIFA Formula


    PVIFA(ytm%, n) = [1 - v] / ytm%
    v = 1 / (1 + ytm%)^n
    PVIFA(ytm%, n) = [1 - { 1 / (1 + ytm%)^n }] / ytm%

    PVIFA Calculation


    v = 1 / (1+0.055)^40
    v = 0.117463142305
    PVIFA(0.055, 40) = [1 - 0.117463142305] / 0.055
    PVIFA(0.055, 40) = 0.882536857695 / 0.055
    PVIFA(0.055, 40) = 16.0461246854
    PVIF Formula

    PVIF(ytm%, n) = 1 / (1 + ytm%)^n
    PVIF Calculation

    PVIF(0.055, 40) = 1 / (1+0.055)^40
    PVIF(0.055, 40) = 1 / 8.51330877398
    PVIF(0.055, 40) = 0.117463142305
    Non Zero Bond Price Calculation

    Price = 0.05 x 100 x 16.0461246854 + 100 x 0.117463142305
    Price = 80.2306234269 + 11.7463142305
    Price = $91.98

    Compounding = annually
    Par Value = 100
    Coupon Rate = 0.1
    Market Rate = 0.11
    N = 20

    Non Zero Bond Price Formula

    Coupon Rate x Par Value x PVIFA(ytm%, n) + Par Value x PVIF(ytm%, n)

    PVIFA Formula


    PVIFA(ytm%, n) = [1 - v] / ytm%
    v = 1 / (1 + ytm%)^n
    PVIFA(ytm%, n) = [1 - { 1 / (1 + ytm%)^n }] / ytm%

    PVIFA Calculation


    v = 1 / (1+0.11)^20
    v = 0.12403390709
    PVIFA(0.11, 20) = [1 - 0.12403390709] / 0.11
    PVIFA(0.11, 20) = 0.87596609291 / 0.11
    PVIFA(0.11, 20) = 7.96332811737
    PVIF Formula

    PVIF(ytm%, n) = 1 / (1 + ytm%)^n
    PVIF Calculation

    PVIF(0.11, 20) = 1 / (1+0.11)^20
    PVIF(0.11, 20) = 1 / 8.06231153613
    PVIF(0.11, 20) = 0.12403390709
    Non Zero Bond Price Calculation

    Price = 0.1 x 100 x 7.96332811737 + 100 x 0.12403390709
    Price = 79.6332811737 + 12.403390709
    Price = $92.04

    Reference: Bond Price Calculator
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