the corner grocer has a 7-year, 6 percent annual 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 6.5 percent?
The bond price will increase by $57.14.
The bond price will increase by 5.29 percent.
The bond price will decrease by $53.62.
The bond price will decrease by 5.43 percent.
The bond price will decrease by 5.06 percent.
To determine the correct statement, we need to calculate the current bond price and compare it with the new bond price after the change in market yield.
To calculate the current bond price, we can use the bond pricing formula:
Bond Price = C * [1 - (1 / (1 + r)^n)] / r + (F / (1 + r)^n)
Where:
C = coupon payment per period
r = yield to maturity (YTM) as a decimal
n = number of periods
F = par value or face value of the bond
Given:
C = 0.06 * $1,000 = $60
r = 0.055 (5.5% as a decimal)
n = 7 (since it's a 7-year bond)
F = $1,000
Using the above formula, we can calculate the current bond price:
Bond Price = $60 * [1 - (1 / (1 + 0.055)^7)] / 0.055 + ($1,000 / (1 + 0.055)^7)
Bond Price ≈ $906.87
Now, let's calculate the new bond price after the increase in market yield:
New Bond Price = $60 * [1 - (1 / (1 + 0.065)^7)] / 0.065 + ($1,000 / (1 + 0.065)^7)
New Bond Price ≈ $849.25
Finally, we can compare the current and new bond prices to determine the correct statement:
Bond Price Change = New Bond Price - Current Bond Price
Bond Price Change ≈ $849.25 - $906.87
Bond Price Change ≈ -$57.62
Therefore, the correct statement is: "The bond price will decrease by $57.62."
None of the given options exactly matches this value, so the correct answer is not provided in the options given.