The Corner Grocer has a 7-year, 6.5 percent semiannual coupon bond outstanding with a $1,000 par value. The bond has a yield to maturity of 5.5 percent. Which one of the following statements is correct if the market yield suddenly increases to 7.25 percent?A) The bond price will decrease by 9.27 percent. B) The bond price will increase by 3.86 percent. C) The bond price will decrease by 8.64 percent. D) The bond price will increase by 7.16 percent. E) The bond price will increase by 7.04 percent

Hello, well, it is better that we find the price of the bond before and after the change of discount rate (from 5.5% to 7.25%). But first we have to make the coupon and the discount rate semi-annual.

[tex]Coupon=FaceValue*\frac{CouponRate}{2} =1000*\frac{0.065}{2} =32.5[/tex]

[tex]YTM(Annual)=\frac{YTM(semi-annual)}{2} =\frac{0.055}{2} =0.0275[/tex]

With that in mind, let´s find the original price of the bond.

[tex]Price=\frac{32.5((1+0.0275)^{13} -1)}{0.0275(1+0.0275)^{13} } +\frac{(32.5+1000)}{(1+0.0275)^{14} } =1057.46[/tex]

Now, that was the price of the bond, but the discount rate went up, so the new price of the bond is:

[tex]Price=\frac{32.5((1+0.0363)^{13} -1)}{0.0363(1+0.0363)^{13} } +\frac{(32.5+1000)}{(1+0.0363)^{14} } =959.39[/tex]

That means that the price variation was:

[tex]Variation=\frac{(Final Value-Initial Value)}{InitialValue}[/tex]

[tex]Variation=\frac{(959.39-1057.46)}{1057.64} =-0.0927[/tex]

So the answer is A) The bond price will decrease by 9.27%

Best of luck