2. 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?
Answer: B
The approximate loan balance after the next monthly payment is $49,541.83.
After making the next monthly payment of $854, the loan balance will be approximately $49,541.83, taking into account the interest accrued since the last payment.
A) $49,080.04
This option is incorrect as it underestimates the remaining loan balance. Given the monthly payment and interest rate, the balance should decrease more conservatively, not to such a low figure as $49,080.04.
B) $49,541.83
This option accurately reflects the remaining loan balance after the monthly payment is applied. The calculation considers the interest accrued on the remaining balance and the amount paid towards principal reduction, leading to this precise figure.
C) $49,562.67
This choice is incorrect because it suggests a balance that is too high after accounting for the monthly payment. The calculated interest on the outstanding balance and the payment made would not leave such a high remaining balance.
D) $49,604.17
This option is also incorrect as it indicates a balance that does not align with the expected decrease following the monthly payment. The interest and principal components of the payment do not support such a remaining balance.
Conclusion
The correct answer is $49,541.83, as it accurately reflects the balance after the next payment, which includes the interest that has accrued since the last payment. All other options either overestimate or underestimate the balance due to miscalculations related to interest and principal payments.