Respuesta :
$122.47 is the change in bond price will experience in dollars at 8 percent yield to maturity and 7.5 percent coupon bond.
to calculate duration of the bond using formula:
Duration = [(1+YTM/2) /YTM] - [(1+YTM/2) + M(C-YTM)]/YTM + C[(1+YTM/2)2M - 1]
annual coupon rate, C = 7.5%
yield to maturity ,YTM = 10.4%
bond maturity ,M = 9 years
Duration = [(1+0.104/2)/0.104] - [(1+0.104/2) + 9(0.075-0.104)]/0.104 + 0.075[(1+0.104/2)2 × 9 - 1]
Duration = 10.12 - (0.791)/0.104 + 0.075(2.49 - 1)
= 10.12 - (0.791)/0.104 + 0.112
= 10.12 - (0.791)/0.216
= 10.12 - 3.66
= 6.46 Years
percentage change in bond price = duration change × change in YTM
Modified duration = duration/(1+YTM/2)
= 6.46/(1+0.104/2)
= 6.46/1.052
= 6.14
% change in bond price = 6.14× (0.104 - 0.08)
= 0.147 or 14.7%
Bond price will increase by 14.7%
N= maturity = 9×2 = 18;
I/Y = YTM = 10.4%/2 = 5.2%;
FV = par value = 1,000;
PMT = coupon = 1,000 × 7.5%/2 = 37.5
PV = current price = 833.12
Change in price in dollars = $833.12 × 14.7%
= $122.47
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