Question

Suppose a bond with no expiration date has a face value of \(10,000 and annually pays \)800 in fixed interest. In the table provided below, calculate and enter either the interest rate that the bond would yield to a bond buyer at each of the bond prices listed or the bond price at each of the interest yields shown. What generalization can you draw from the completed table?

Bond Price \( 8,000	Interest Yield, % ________
______	8.9
\)10,000 $11,000 _______	________ ________ 6.2

Short answer

The interest rate of 8% will yield $800 annually for a bond with a face value of $10,000.

At $8000 of bond price, the interest yield is 10%.

At 8.9% of the interest yield, the bond price is $8989.

At $11,000 of bond price, the interest yield is 7.2%.

At 8.9% of the interest yield, the bond price is 12,903.

The interest yield and bond prices are inversely related.

Step-by-step solution

Computing the interest rate

The face value of the bond with no expiration date is $10,000 (given).

At a fixed interest rate, the yield of the bond is $800.

Suppose the interest yield is x.

$$\begin{gathered} thenx\%of10,000=800 \\ x=8\% \end{gathered}$$

Thus, an interest rate of 8% will yield $800 for a bond with a face value of $10,000.

Completed table of bond price and interest yield

At $8000 of bond price, the interest yield is

$$\begin{gathered} \frac{x}{100}\times 8000=800 \\ x=10 \end{gathered}$$

The interest yield is 10%.

At 8.9% of the interest yield, the bond price is

$$\begin{gathered} \frac{8.9}{100}\times x=800 \\ x=8989 \end{gathered}$$

The bond price is $8989.

At $11,000 of bond price, the interest yield is

$$\begin{gathered} \frac{x}{100}\times 11000=800 \\ x=7.2 \end{gathered}$$

The interest yield is 7.2%.

At 6.2% of the interest yield, the bond price is

$$\begin{gathered} \frac{6.2}{100}\times x=800 \\ x=12903 \end{gathered}$$

The bond price is $12,903.

The completed table is shown below:

Bond Price $ 8,000	Interest Yield, % 10
$ 8,989	8.9
$10,000 $11,000 $12,903	8.0 7.2 6.2

Interpretation from the values of the table

This is evident from the table obtained in step 2. As the interest yield increases from 6.2% to 10%, the bond prices decrease from $12,903 to $8,000.