If a bond has a par value of $1,000 and a coupon of 6%, what is the nominal value (in dollars) of the bond if the current interest rate is 5.5%? Round to the nearest dollar.
show your work
To calculate the nominal value of the bond, we need to find the present value of the bond's future cash flows (coupon payments and the face value) discounted at the current interest rate.
PV = C * (1 - (1 / (1 + r)^n) / r + FV / (1 + r)^n
Where:
PV = Present value of the bond
C = Annual coupon payment = Par value * Coupon rate = $1,000 * 6% = $60
r = Current interest rate = 5.5% or 0.055
n = Number of years until the bond matures = 1
FV = Face value or par value of the bond = $1,000
Plugging in the values:
PV = $60 * (1 - (1 / (1 + 0.055)^1) / 0.055 + $1,000 / (1 + 0.055)^1
PV = $60 * (1 - (1 / 1.055) / 0.055 + $1,000 / 1.055
PV = $60 * (1 - 0.94862 / 0.055 + $948.62
PV = $60 * (18.3928 + $948.62)
PV = $60 * $966.01
PV = $57,960.60
Rounding to the nearest dollar, the nominal value of the bond is $57,961.