To find the yield on a corporate bond, follow these steps:
1. Identify the given data:
- Face value of the bond: \[tex]$1000
- Discount price (the price at which the bond is purchased): \$[/tex]950
- Fixed interest rate: 5%
2. Calculate the annual interest paid by the bond:
The annual interest paid is calculated as:
[tex]\[
\text{interest paid} = \text{face value} \times \text{interest rate}
\][/tex]
Given the face value is \$1000 and the interest rate is 5%, we get:
[tex]\[
\text{interest paid} = 1000 \times 0.05 = 50 \, \text{dollars}
\][/tex]
3. Determine the formula for yield:
The yield is calculated as the annual interest paid divided by the discount price, expressed as a percentage. The formula is:
[tex]\[
\text{yield percentage} = \left( \frac{\text{interest paid}}{\text{price paid}} \right) \times 100
\][/tex]
4. Substitute the values into the formula:
[tex]\[
\text{yield percentage} = \left( \frac{50}{950} \right) \times 100
\][/tex]
5. Simplify the expression:
[tex]\[
\text{yield percentage} = \left( \frac{50}{950} \right) \times 100 = \left( 0.0526315789 \right) \times 100 \approx 5.26\%
\][/tex]
6. Round to the nearest hundredth of a percent:
Upon rounding, we find that:
[tex]\[
\text{yield percentage} \approx 5.26\%
\][/tex]
Therefore, the yield on the corporate bond is [tex]\( 5.26\% \)[/tex].
