Final answer:
The carrying value of the bonds on January 1, 20x4, using the straight-line method of amortization, is $431,500 after accounting for three years of premium amortization.
Step-by-step explanation:
The subject of the question is to calculate the carrying value of bonds using the straight-line method of amortization. To answer this, we must first determine the bond premium by subtracting the face value from the proceeds. The initial premium is $45,000 ($445,000 proceeds - $400,000 face value). As the bonds mature over 10 years, this premium is amortized evenly each year, which gives us an annual amortization of $4,500 ($45,000 / 10 years). By January 1, 20x4, three years have passed, so a total of $13,500 ($4,500 x 3 years) has been amortized. Therefore, the carrying value of the bond on January 1, 20x4, would be the face value of $400,000 plus the unamortized premium, which is the initial premium minus the amount already amortized: $445,000 - $13,500 = $431,500.