To determine which statement is true for bonds issued at a premium, we need to understand the relationship between the stated interest rate (coupon rate) and the market interest rate.
### Concepts:
1. Stated Interest Rate (Coupon Rate): This is the interest rate that the bond issuer agrees to pay bondholders, usually expressed as a percentage of the bond's face value.
2. Market Interest Rate: This is the rate of interest currently prevailing in the market for similar bonds.
### Bonds Issued at a Premium:
- Issuing a Bond at a Premium: When bonds are sold for more than their face value, they are said to be issued at a premium. This happens because the bond’s stated interest rate is more attractive than the market interest rate.
### Detailed Explanation:
1. If the stated interest rate were less than the market interest rate, investors would not be interested in buying the bond at a price higher than its face value, because they could get a better return elsewhere.
2. If the stated interest rate and the market interest rate were equal, the bond would sell at its face value, not at a premium.
3. The interest rates being unrelated is not a practical scenario in the bond market, as the relationship between stated rates and market rates is fundamental to bond pricing.
### Correct Scenario:
When the market interest rate is less than the stated interest rate, the bond becomes more attractive because it offers a higher return compared to the market rate. This increased demand allows the issuer to sell the bond at a premium.
Therefore, the correct statement is:
- The market interest rate is less than the stated interest rate.
Thus, the answer is:
```
The market interest rate is less than the stated interest rate.
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