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.)

Answer 1

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.