To determine the market annual interest rate for the bonds, we can use the information provided in the amortization schedule. We will focus on the bond's interest payments, the interest expense, and the carrying value to calculate the effective interest rate.

Key Information:

• The cash paid (semi-annual interest payment) on June 30, 2021 is $600,000.
• The interest expense for the period is $420,000.
• The bond's carrying value as of January 1, 2021 is $12,000,000, and it increases to $12,180,000 after the first semi-annual period (due to amortization).

We know the effective interest rate (market rate) is applied to the bond's carrying value to calculate the interest expense. This formula will help us find the semi-annual market interest rate:

$\text{Interest Expense} = \text{Carrying Value} \times \text{Market Semi-Annual Rate}$

Rearranging the formula to solve for the semi-annual rate:

$\text{Market Semi-Annual Rate} = \frac{\text{Interest Expense}}{\text{Carrying Value}}$

Using the given dataTo determine the market annual interest rate for the bonds, we can use the information provided in the amortization schedule. We will focus on the bond's interest payments, the interest expense, and the carrying value to calculate the effective interest rate.

Key Information:

• The cash paid (semi-annual interest payment) on June 30, 2021 is $600,000.
• The interest expense for the period is $420,000.
• The bond's carrying value as of January 1, 2021 is $12,000,000, and it increases to $12,180,000 after the first semi-annual period (due to amortization).

We know the effective interest rate (market rate) is applied to the bond's carrying value to calculate the interest expense. This formula will help us find the semi-annual market interest rate:

$\text{Interest Expense} = \text{Carrying Value} \times \text{Market Semi-Annual Rate}$

Rearranging the formula to solve for the semi-annual rate:

$\text{Market Semi-Annual Rate} = \frac{\text{Interest Expense}}{\text{Carrying Value}}$

Using the given $\text{Market Semi-Annual Rate} = \frac{420,000}{12,000,000} = 0.035 \text{ or } 3.5\%$

Since the interest is paid semi-annually, the annual market interest rate would be double the semi-annual rate:

$\text{Annual Market Interest Rate} = 2 \times 3.5\% = 7\%$

Conclusion:

The market annual interest rate is 7%.

Would you like further details on this calculation or clarification on any steps?

Here are 5 related questions to explore:

1. How is the carrying value of a bond determined over time?
2. What is the difference between nominal interest rate and effective interest rate?
3. How does bond amortization affect financial statements?
4. Why are bonds issued at a discount or premium?
5. How do market interest rates influence bond prices?

Tip: The effective interest method for amortizing bond premiums or discounts more accurately reflects the cost of borrowing than the straight-line method.