The bond quote of a 15-year, 7 percent, semi-annual coupon bond when the market rate is 11 percent is closest to:

Question

Quizplus · Accepted Answer

The bond quote represents the present value of the bond's future cash flows, discounted at the market rate. For a semi-annual coupon bond, the coupon payment is 7% of the face value (assumed to be $1000 here) divided by 2, because of the semi-annual payments, which equals $35. The market rate of 11% also needs to be halved for the semi-annual calculation, making it 5.5%. The bond's price 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 face value at maturity). The calculation is as follows:$$ \text{Bond price} = \frac{C}{r} \left(1 - \frac{1}{(1+r)^{n}}\right) + \frac{F}{(1+r)^{n}} $$Where:- $C$ is the semi-annual coupon payment ($35),- $r$ is the semi-annual market rate (5.5% or 0.055),- $n$ is the total number of semi-annual periods (15 years * 2 = 30),- $F$ is the face value of the bond ($1000).$$ \text{Bond price} = \frac{35}{0.055} \left(1 - \frac{1}{(1+0.055)^{30}}\right) + \frac{1000}{(1+0.055)^{30}} $$$$ \text{Bond price} \approx 70.93 $$Therefore, the bond quote is closest to 70.93, making option A correct.

The Bond Quote of a 15-Year, 7 Percent, Semi-Annual Coupon