Calculate the premium or discount on the sale of a 20-year, $10,000 Rogers Communications Corp. bond that was issued nine years ago with a coupon rate of 9% and is trading today at a yield rate of 8.0% (compounded semiannually).

Question

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The bond is trading at a premium because its coupon rate (9%) is higher than its current yield rate (8%). To calculate the premium, we first find the present value of the bond's remaining cash flows (interest payments and the principal repayment) discounted at the current yield rate. The bond has 11 years left until maturity (20 - 9 = 11), with semiannual interest payments (9% of $10,000 = $900 annually or $450 semiannually) and a face value of $10,000. Using the formula for the present value of an annuity and the present value of a lump sum, we calculate the bond's price and compare it to its face value to determine the premium.

Calculate the Premium or Discount on the Sale of a 20-Year