Calculate the premium or discount on the sale of a 30-year, $1,000 General Motors bond that was issued 21 years ago with a coupon rate of 16% and is trading today at a yield rate of 6.5% (compounded semiannually).

Question

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The bond is trading at a premium because its coupon rate (16%) is significantly higher than the current yield rate (6.5%). To calculate the exact premium, we use the present value of the bond's remaining cash flows (interest payments and principal repayment) discounted at the current yield rate. Given the bond's semiannual interest payments, its annual coupon payment is $160 (16% of $1,000), or $80 per semiannual period. With 18 years (36 periods) remaining, the present value of the bond can be calculated using the formula for the present value of an annuity (for the coupon payments) plus the present value of a lump sum (for the bond's principal repayment at maturity). The calculation shows that the bond's value exceeds its face value, indicating a premium. The exact amount of the premium can be determined by comparing the calculated present value to the bond's original face value of $1,000, leading to the correct option.

Calculate the Premium or Discount on the Sale of a 30-Year