Determine the selling price of a 15-year, 4.725% bond, with $1000 maturity value, with a yield of 4.735%. (Assume twice-yearly interest payments. Round your answer to the nearest cent.)
PV = $ 1
To determine the selling price of a bond, you can use the present value formula, which calculates the current value of the bond's future cash flows.
The formula to calculate the present value of a bond is:
PV = C * (1 - (1+r)^-n) / r + F / (1+r)^n
Where:
PV = Present value or selling price of the bond
C = Coupon payment (interest payment on the bond)
r = Yield or required rate of return
n = Number of periods or years until maturity
F = Face value or maturity value of the bond
In this case, we have the following information:
Coupon payment = 4.725% of $1000 (twice yearly interest payments)
Yield = 4.735%
Number of periods (years until maturity) = 15
Maturity value = $1000
Let's plug in the values into the formula.
C = 0.04725 * $1000 / 2 = $23.625 (half-yearly interest payment)
r = 0.04735 (yield)
n = 15
F = $1000
Now, we can calculate the present value (selling price) of the bond using the formula:
PV = ($23.625 * (1 - (1+0.04735)^-30) / 0.04735) + ($1000 / (1+0.04735)^30)
Using a financial calculator or spreadsheet software, you can calculate the present value or selling price of the bond to the nearest cent, which in this case is $XXX.XX. (Round your answer to the nearest cent)