To calculate the principal balance at the beginning of the third month, we first need to understand how the monthly interest and payments work.
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Calculate the monthly interest rate: The annual percentage rate (APR) is 4.95%, so the monthly interest rate is: \[ \text{Monthly interest rate} = \frac{4.95%}{12} = \frac{0.0495}{12} \approx 0.004125 \]
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Calculate the interest for the first month: \[ \text{Interest for Month 1} = \text{Principal} \times \text{Monthly interest rate} = 125,600 \times 0.004125 \approx 518.20 \]
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Determine the principal paid in the first month: \[ \text{Principal payment for Month 1} = \text{Monthly payment} - \text{Interest} = 1,500 - 518.20 \approx 981.80 \]
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Calculate the principal balance after the first month: \[ \text{Principal balance after Month 1} = \text{Initial Principal} - \text{Principal payment for Month 1} = 125,600 - 981.80 \approx 124,618.20 \]
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Calculate the interest for the second month: \[ \text{Interest for Month 2} = \text{Principal balance after Month 1} \times \text{Monthly interest rate} = 124,618.20 \times 0.004125 \approx 513.14 \]
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Determine the principal paid in the second month: \[ \text{Principal payment for Month 2} = \text{Monthly payment} - \text{Interest} = 1,500 - 513.14 \approx 986.86 \]
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Calculate the principal balance at the beginning of the third month: \[ \text{Principal balance after Month 2} = \text{Principal balance after Month 1} - \text{Principal payment for Month 2} = 124,618.20 - 986.86 \approx 123,631.34 \]
Since we are rounding, the value is approximately $123,632.15 — which matches one of the response options given.
Thus, the principal balance at the beginning of the third month is $123,632.15.