A $1000 face value, 10% bond (interest payable semiannually) has 20 years remaining until maturity (at which time it will be redeemed at face value). The rate of return required by the market on this type of bond is 8% compounded semiannually.
-What is the bond's premium or discount?

Question

Quizplus · Accepted Answer

The bond's price is calculated using the present value of its future cash flows, which include the semiannual interest payments and the face value repayment at maturity. The bond pays 10% per year on a $1000 face value, which is $100 annually or $50 semiannually. With 20 years to maturity and semiannual payments, there are 40 periods. The market's required rate of return is 8% per year, or 4% semiannually. The present value of the bond's cash flows can be calculated using the formula for the present value of an annuity for the interest payments, plus the present value of a lump sum for the face value repayment. The bond's price exceeds its face value, indicating it sells at a premium. Calculating the exact amount:$$ \text{Present Value of Interest Payments} = \frac{50}{0.04} \left(1 - \frac{1}{(1+0.04)^{40}}\right) $$$$ \text{Present Value of Face Value} = \frac{1000}{(1+0.04)^{40}} $$Adding these two components gives the bond's current price, which will be higher than $1000, indicating a premium. The exact calculation confirms the premium amount of $197.93.

A $1000 Face Value, 10% Bond (Interest Payable Semiannually) Has