Final answer:
The carrying value of the bonds after the first interest payment is $571,776. This is calculated by amortizing the bond premium based on the interest expense using the market rate and subtracting it from the initial carrying amount of the bonds.
Step-by-step explanation:
To calculate the carrying value of the bonds after the first interest payment, you need to account for the bond premium amortization. The bonds were issued at a premium because the market interest rate of 6% is less than the face rate of 8%. The bond's annual interest payment is $500,000 x 8% = $40,000, paid semi-annually, which means every six months the payment will be $20,000.
Since the bonds were issued at a premium, this premium is amortized over the life of the bond. The premium amortization for each period is calculated using the effective interest method or a straight-line method, but the effective interest method is more accurate.
Assuming we are using the effective interest method, we first calculate the interest expense based on the carrying amount of the bond and the market rate. For the first six months, this would be $574,540 x 6% x (6/12) = $17,236.20. The difference between the actual cash paid for interest and the interest expense is the amount of premium amortized.
The premium amortized in this period is $20,000 (cash interest paid) - $17,236.20 (interest expense) = $2,763.80. To find the new carrying value after this payment and amortization, subtract the amortized premium from the initial carrying amount: $574,540 - $2,763.80 = $571,776.20. Thus, the correct answer for the carrying value of the bonds after the first interest payment is $571,776.