The Corner Grocer has a 7-year, 6 percent annual coupon bondoutstanding with a $

Question

The Corner Grocer has a 7-year, 6 percent annual coupon bondoutstanding with a $1,000 par value. The bond has a yield tomaturity of 5.5 percent. Which one of the following statements iscorrect if the market yield suddenly increases to 6.5 percent? The bond price will increase by $57.14. The bond price will increase by 5.29percent. The bond price will decrease by $53.62. The bond price will decrease by 5.43percent. The bond price will decrease by 5.36percent. The bond price will increase by $57.14. The bond price will increase by 5.29percent. The bond price will decrease by $53.62. The bond price will decrease by 5.43percent. The bond price will decrease by 5.36percent. The bond price will increase by $57.14. The bond price will increase by 5.29percent. The bond price will decrease by $53.62. The bond price will decrease by 5.43percent. The bond price will decrease by 5.36percent.

Explanation / Answer

7 years

7 years

Annual Coupon Amount($1,000 * 6%) $60 Yield to Maturity ( r) 5.50% Par Value (or) Face Value of thebond (F) $1,000 Number of Years to Maturity(t)

7 years

Bond Value = C *[1-1/(1+r)t] / r +F/(1+r)t Bond Value = $60 *[1-1/(1+0.055)7] / 0.055 + $1,000 /(1+0.055)7 Bond Value = $60 *[1-1/(1.055)7] / 0.055 + $1,000 /(1.055)7 Bond Value = $60 *[1-1/1.454679161] / 0.055 + [$1,000/1.454679161] BondValue = $60 * [1-0.687436808] /0.055 + $687.44 Bond Value = $60 *[5.682967] + $687.44 Bond Value = $340.98 +$687.44 Fair Value of theBond = $1,028.42 Annual Coupon Amount ($1,000 *6%) $60 Yield to Maturity ( r) 6.50% Par Value (or) Face Value of thebond (F) $1,000 Number of Years to Maturity(t)

7 years

Bond Value = C *[1-1/(1+r)t] / r + F/(1+r)t Bond Value = $60 *[1-1/(1+0.065)7] / 0.065 + $1,000 /(1+0.065)7 Bond Value = $60 *[1-1/(1.065)7] / 0.065 + $1,000 /(1.065)7 Bond Value = $60 *[1-1/1.553986546] / 0.065 + [$1,000/1.553986546] Bond Value = $60 *[1-0.6435] / 0.065 + $643.50 Bond Value = $60 *[5.48461538] + $643.50 Bond Value = $329.07 +$643.50 Fair Value of theBond = $972.57 The Bond Price willdecrease by = [($1,028.42 - $972.57) / $972.57] The Bond Price willdecrease by = 5.74%(approximately)

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