I am having a problem with this question and need direction.A $500 8% bond is purchased on Feb. 1,2004 to yield 10% compounded semi-annually. The interest on the bond is payable on Feb. 1 and Aug.1 each year. What is the purchase price if the bond is redeemable at face value on Feb. 1, 2014? I don't even know where to start and can't find any samples in my text. Thank you very much for any help.
To find the purchase price of a bond, we need to use the present value formula, which takes into account the future value, interest rate, and time period.
In this case, the bond has a face value (or future value) of $500, an 8% annual interest rate (or coupon rate), and a yield (or discount rate) of 10% compounded semi-annually. The interest is payable on Feb. 1 and Aug. 1 each year.
To begin solving this problem, we first need to find the number of periods (n) the bond runs for. Since it was purchased on Feb. 1, 2004, and redeemable on Feb. 1, 2014, the bond runs for 10 years or 20 semi-annual periods (2 periods per year).
Next, we need to find the interest payment for each period. Since the coupon rate is 8% and the face value is $500, the annual interest payment is 0.08 * $500 = $40. Since the interest is paid semi-annually, the interest payment per period is $40/2 = $20.
Now, we have all the information needed to apply the present value formula:
Purchase Price = (Interest Payment / (1 + Yield Rate/2)^n) + (Face Value / (1 + Yield Rate/2)^n)
Plugging in the values:
Purchase Price = ($20 / (1 + 0.10/2)^20) + ($500 / (1 + 0.10/2)^20)
Now, we can calculate the Purchase Price using either a financial calculator or spreadsheet software. The result will be the purchase price of the bond.