Final answer:
Using the effective-interest method, the amount of premium amortized in the first year is the difference between the bond's interest payment and the interest expense calculated using the market rate. Consequently, the carrying amount of the bond at the end of the first year is $3,184,500.
Step-by-step explanation:
On January 1, Martinez Inc. issued $3,000,000, 11% bonds for $3,195,000. The bond was issued at a premium because the stated interest rate of the bond is higher than the market interest rate. The premium on the bonds payable is the difference between the issuance price and the face value, which in this case is $195,000. Since Martinez uses the effective-interest method of amortizing the bond premium, we must calculate the interest expense based on the market rate and then determine the premium amortization for the first year.
The interest payment for the first year is $3,000,000 × 11% = $330,000. However, the interest expense is based on the market rate of 10% of the carrying amount of the bond. So, at the beginning, the carrying amount is $3,195,000 (the price it was sold for), and the interest expense is $3,195,000 × 10% = $319,500. The amount of premium amortized in the first year is the difference between the interest payment and the interest expense: $330,000 - $319,500 = $10,500.
Therefore, the carrying amount of the bond at the end of the first year is $3,195,000 - $10,500 = $3,184,500.