Final answer:
The interest included in the 48th payment of the mortgage loan is approximately $2,103.16.
Step-by-step explanation:
To calculate the interest included in the 48th payment, we first need to find the monthly payment for the mortgage loan. The formula to calculate the monthly payment for an amortized loan is:
Monthly Payment = P * r * (1 + r)n / ((1 + r)n - 1)
Where:
- P = Principal amount = $132,000
- r = Monthly interest rate = Annual interest rate / Number of compounding periods per year = 7% / 2 = 0.035
- n = Total number of payments = 25 * 12 = 300
Plugging in the values, we get:
Monthly Payment = $132,000 * 0.035 * (1 + 0.035)300 / ((1 + 0.035)300 - 1) ≈ $868.31
To find the interest included in the 48th payment, we can use the formula:
Interest = Outstanding Balance * Monthly interest rate
At the start of the 48th payment, the outstanding balance can be calculated as the remaining balance after 47 payments:
Outstanding Balance = Principal amount - (Principal amount * [(1 + r)n - (1 + r)p]) / ((1 + r)n - 1)
Where p = Number of payments made = 47
Plugging in the values, we get:
Outstanding Balance = $132,000 - ($132,000 * [(1 + 0.035)300 - (1 + 0.035)47]) / ((1 + 0.035)300 - 1) ≈ $60,118.68
Now we can calculate the interest included in the 48th payment:
Interest = $60,118.68 * 0.035 ≈ $2,103.16
Therefore, the answer is not among the given options. The correct answer is approximately $2,103.16.