Final answer:
The issue price for the bonds is $705,109.
Step-by-step explanation:
To calculate the issue price of the bonds, we need to calculate the present value of the future cash flows. The cash flows for the bonds are the periodic interest payments and the final principal payment at maturity. The present value factor is calculated using the market interest rate and the number of periods until each cash flow is received. The formula to calculate the present value factor is given by:
Present value factor = 1 / (1 + r/n)^(n*t)
Where r is the market interest rate, n is the number of compounding periods per year, and t is the number of years until each cash flow is received.
First, let's calculate the present value of the interest payments:
Annual interest payment = Bond face value * Coupon rate = $590,000 * 9% = $53,100
Semiannual interest payment = Annual interest payment / 2 = $53,100 / 2 = $26,550
Number of periods = Number of years * Number of compounding periods per year = 10 * 2 = 20
Present value factor for each semiannual interest payment = 1 / (1 + 10%/2)^(2*1) = 1 / (1 + 5%)^2 = 1 / 1.05^2 = 0.90703
Total present value of the interest payments = Present value factor * Semiannual interest payment * Number of periods = 0.90703 * $26,550 * 20 = $483,007
Next, let's calculate the present value of the final principal payment:
Present value factor for the principal payment at maturity = 1 / (1 + 10%/2)^(2*10) = 1 / (1 + 5%)^20 = 1 / 1.05^20 = 0.37689
Present value of the principal payment = Present value factor * Bond face value = 0.37689 * $590,000 = $222,102
The issue price of the bonds is the sum of the present values of the interest payments and the principal payment:
Issue price = Total present value of interest payments + Present value of principal payment = $483,007 + $222,102 = $705,109