Question

You have a mortgage of $125,600.00 at a 4.95% APR. You make a payment of $1,500.00 each month. What is your principal balance at the beginning of the third month?
(1 point)
Responses

$122,600.00
$122,600.00

$123,632.15
$123,632.15

$123,636.20
$123,636.20

$122,654.30

Answer 1

To calculate the principal balance at the beginning of the third month, we first need to understand how the monthly interest and payments work.

1. **Calculate the monthly interest rate:**
The annual percentage rate (APR) is 4.95%, so the monthly interest rate is:
\[
\text{Monthly interest rate} = \frac{4.95\%}{12} = \frac{0.0495}{12} \approx 0.004125
\]

2. **Calculate the interest for the first month:**
\[
\text{Interest for Month 1} = \text{Principal} \times \text{Monthly interest rate} = 125,600 \times 0.004125 \approx 518.20
\]

3. **Determine the principal paid in the first month:**
\[
\text{Principal payment for Month 1} = \text{Monthly payment} - \text{Interest} = 1,500 - 518.20 \approx 981.80
\]

4. **Calculate the principal balance after the first month:**
\[
\text{Principal balance after Month 1} = \text{Initial Principal} - \text{Principal payment for Month 1} = 125,600 - 981.80 \approx 124,618.20
\]

5. **Calculate the interest for the second month:**
\[
\text{Interest for Month 2} = \text{Principal balance after Month 1} \times \text{Monthly interest rate} = 124,618.20 \times 0.004125 \approx 513.14
\]

6. **Determine the principal paid in the second month:**
\[
\text{Principal payment for Month 2} = \text{Monthly payment} - \text{Interest} = 1,500 - 513.14 \approx 986.86
\]

7. **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**.