Final answer:
The principal balance of the term installment loan on January 1, Year 2, would be $166,581 after the first payment, however, this is not reflected in the given answer choices, suggesting there may be a typo in the options provided.
Step-by-step explanation:
The question is asking for the principal balance of a term installment loan after the first annual payment has been made. On January 1, Year 1, Zoe Company issued a $200,000, 9%, 5-year term installment loan, and the first annual payment of $51,419 is made on December 31, Year 1. To find the principal balance on January 1, Year 2, we must deduct the portion of the first payment that went towards the principal from the original loan amount.
First, we need to calculate the interest portion of the first payment:
Interest for Year 1 = Principal × Interest rate = $200,000 × 9% = $18,000.
Next, we deduct the interest from the total payment to find out how much of the payment was applied to the principal:
Principal Repaid in Year 1 = Total payment - Interest payment = $51,419 - $18,000 = $33,419.
Finally, we subtract the principal repaid in Year 1 from the original loan amount to find the principal balance:
Principal balance on January 1, Year 2 = Original principal - Principal repaid = $200,000 - $33,419 = $166,581.
However, none of the answer choices matches this calculation. Therefore, it's possible there may be a typo or mistake in the answer choices provided. Based on correct calculations, the answer would be $166,581, but this is not an option given. Thus, we cannot choose from the available options A) $0, B) $51,419, C) $148,581, D) $200,000.