Final Answer:
The market interest rate was less than the bonds' contractual interest rate.
Step-by-step explanation:
When bonds are sold at a premium (above their face value), it implies that the contractual interest rate (also known as the coupon rate) is higher than the prevailing market interest rate. Here's how the calculation works:
Given:
Face value of bonds = $100,000
Sale price of bonds = $104,000
To find the premium:
Premium = Sale price of bonds - Face value of bonds
Premium = $104,000 - $100,000 = $4,000
Now, to understand the relationship between the market interest rate and the contractual interest rate, we can use the fact that the premium exists because the contractual interest rate is higher.
For instance, if the bonds were sold at face value ($100,000), it would mean the market interest rate equals the contractual interest rate. However, as the bonds were sold at a premium of $4,000, it implies investors were willing to pay more for these bonds due to the higher interest rate they offered compared to the prevailing market rates.
Therefore, the premium of $4,000 indicates that the contractual interest rate is higher than the market interest rate. This is why investors were willing to pay more than the face value to secure a higher return from the bonds' interest payments.
This calculation suggests that the market interest rate was indeed less than the bonds' contractual interest rate, as evidenced by the premium paid for the bonds above their face value.