Question
On January 1, 2024, Westside Sales issued $ 24000 in bonds for $ 25800. These are eight-year bonds with a stated interest rate of 12% that pay semiannual interest. Westside Sales uses the straight-line method to amortize the bond premium. After the first interest payment on June 30, 2024, what is the bond carrying amount? (Round your intermediate answers to the nearest dollar.)
Answers
GPT-4o mini
To calculate the bond carrying amount after the first interest payment, we can follow these steps:
1. **Determine the bond premium:**
The bond was issued at $25,800, but its face value is $24,000.
\[
\text{Bond Premium} = \text{Issue Price} - \text{Face Value} = 25,800 - 24,000 = 1,800.
\]
2. **Calculate the total interest payment:**
The bonds have a stated interest rate of 12% per annum and pay interest semiannually.
\[
\text{Semiannual Interest Payment} = \frac{\text{Face Value} \times \text{Stated Interest Rate}}{2} = \frac{24,000 \times 0.12}{2} = 1,440.
\]
3. **Amortize the bond premium:**
Since the bonds have a total life of 8 years with semiannual payments, there will be 16 interest payments. Hence, the annual amortization amount is calculated as:
\[
\text{Premium Amortization per Period} = \frac{\text{Bond Premium}}{\text{Total Number of Periods}} = \frac{1,800}{16} = 112.50.
\]
4. **Calculate the carrying amount after the first interest payment:**
The bond carrying amount at the beginning (January 1, 2024) is the issue price ($25,800).
After the first interest payment (June 30, 2024), the carrying amount will be reduced by the amortized premium:
\[
\text{Carrying Amount} = \text{Initial Carrying Amount} - \text{Amortization} = 25,800 - 112.50 = 25,687.50.
\]
Finally, rounding to the nearest dollar gives us:
\[
\text{Carrying Amount} = 25,688.
\]
So, after the first interest payment on June 30, 2024, the bond carrying amount is **$25,688**.
1. **Determine the bond premium:**
The bond was issued at $25,800, but its face value is $24,000.
\[
\text{Bond Premium} = \text{Issue Price} - \text{Face Value} = 25,800 - 24,000 = 1,800.
\]
2. **Calculate the total interest payment:**
The bonds have a stated interest rate of 12% per annum and pay interest semiannually.
\[
\text{Semiannual Interest Payment} = \frac{\text{Face Value} \times \text{Stated Interest Rate}}{2} = \frac{24,000 \times 0.12}{2} = 1,440.
\]
3. **Amortize the bond premium:**
Since the bonds have a total life of 8 years with semiannual payments, there will be 16 interest payments. Hence, the annual amortization amount is calculated as:
\[
\text{Premium Amortization per Period} = \frac{\text{Bond Premium}}{\text{Total Number of Periods}} = \frac{1,800}{16} = 112.50.
\]
4. **Calculate the carrying amount after the first interest payment:**
The bond carrying amount at the beginning (January 1, 2024) is the issue price ($25,800).
After the first interest payment (June 30, 2024), the carrying amount will be reduced by the amortized premium:
\[
\text{Carrying Amount} = \text{Initial Carrying Amount} - \text{Amortization} = 25,800 - 112.50 = 25,687.50.
\]
Finally, rounding to the nearest dollar gives us:
\[
\text{Carrying Amount} = 25,688.
\]
So, after the first interest payment on June 30, 2024, the bond carrying amount is **$25,688**.