A borrower has a $50,000 mortgage balance. The monthly payment on this loan is $854 and includes interest in arrears at the nominal rate of 9.5% per annum. What is the approximate loan balance after the next monthly payment?

Rationale

The approximate loan balance after the next monthly payment is $49,541.83.

To determine the loan balance after the next monthly payment, we calculate the interest accrued and subtract the principal portion of the payment from the original balance. At a nominal rate of 9.5% per annum, the monthly interest rate is approximately 0.79167%, which leads us to the correct loan balance.

A ($49,080.04) YOUR ANSWER

This option underestimates the loan balance after the payment, as it implies a significantly higher principal reduction than what occurs when accounting for the interest charged on the outstanding balance of $50,000.

B ($49,541.83) CORRECT

This is the correct answer. After applying the monthly interest to the remaining balance and deducting the monthly payment amount, we arrive at this balance, reflecting the accurate principal reduction after interest is accounted for.

C ($49,562.67) YOUR ANSWER

This choice suggests a smaller decrease in the loan balance than is accurate. It does not properly calculate the interest accrued for the month, leading to an inflated balance that doesn't align with the calculated reduction from the total monthly payment.

D ($49,604.17) YOUR ANSWER

This option indicates a minimal reduction in the loan balance, implying that a larger portion of the monthly payment was allocated toward interest rather than the principal. Such a balance would not accurately reflect the payment distribution based on the original loan conditions.

Conclusion

In summary, after the next monthly payment of $854, the accurate loan balance is $49,541.83, taking into consideration the interest accrued on the mortgage. The other options fail to correctly account for the interest portion of the payment or miscalculate the remaining balance, leading to incorrect figures. Understanding these calculations is crucial for effective mortgage management and financial planning.

A borrower has a $50,000 mortgage balance. The monthly payment on this loan is $854 and includes interest in arrears at the nominal rate of 9.5% per annum. What is the approximate loan balance after the next monthly payment?

The approximate loan balance after the next monthly payment is $49,541.83.

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