Final answer:
To determine the interest expense for the second payment of XYZ Corp's loan, one calculates the monthly interest on the remaining loan balance after the first payment. Assuming no principal was paid off with the first payment, the interest expense for the second payment would be approximately $3,333.50.
Step-by-step explanation:
To calculate the amount of interest expense recorded with the second payment on a loan, one must understand how amortizing loans work. The payment each month is fixed, but the portion that goes towards interest versus principal changes because the interest is calculated on the remaining balance of the loan, which decreases with each payment.
For XYZ Corp's second payment on 3/1/X1 for a $500,000 mortgage at 8% annual interest compounding monthly, we need first to calculate the interest portion of the second payment. Since payments are made on the 1st of each month and interest accrues monthly, the interest for the second payment is based on the remaining balance after the first payment.
Here's the step-by-step calculation:
- Calculate the monthly interest rate by dividing the annual rate by 12. This gives 0.08 / 12 = 0.006667 or 0.6667% per month.
- Calculate the interest for the second month. The remaining balance after the first payment is the initial loan amount minus the principal part of the first payment. Since the question does not provide the principal paid in the first month, we will assume the entire first payment was interest. This assumption results in a remaining balance of $500,000 for the second month (this is a simplification for the purpose of this example; in reality, part of the first payment would lower the principal).
- The interest for the second month is then $500,000 x 0.006667 = $3,333.50.
Thus, the amount of interest expense XYZ Corp would record with the second payment would be approximately $3,333.50.