Sure! Let's break down the components of the first mortgage payment to determine how much will go towards the principal.
### Step 1: Define the Given Information
- Principal: \[tex]$150,000
- Annual Interest Rate: 4% (or 0.04)
- Monthly Payment: \$[/tex]716
### Step 2: Convert Annual Interest Rate to Monthly Interest Rate
The interest is compounded monthly, so we need to convert the annual interest rate to a monthly interest rate:
[tex]\[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} \][/tex]
[tex]\[ \text{Monthly Interest Rate} = \frac{0.04}{12} = 0.0033333... \][/tex]
### Step 3: Calculate the Interest Portion of the First Payment
The interest portion of the monthly payment is calculated using the principal amount and the monthly interest rate:
[tex]\[ \text{First Month Interest} = \text{Principal} \times \text{Monthly Interest Rate} \][/tex]
[tex]\[ \text{First Month Interest} = 150{,}000 \times 0.0033333... \][/tex]
[tex]\[ \text{First Month Interest} = 500.00 \][/tex]
### Step 4: Calculate the Principal Portion of the First Payment
To find out how much of the first payment goes towards the principal, we subtract the interest portion from the total monthly payment:
[tex]\[ \text{Principal Portion of First Payment} = \text{Monthly Payment} - \text{First Month Interest} \][/tex]
[tex]\[ \text{Principal Portion of First Payment} = 716 - 500 \][/tex]
[tex]\[ \text{Principal Portion of First Payment} = 216.00 \][/tex]
### Conclusion
Therefore, \[tex]$216.00 of the first payment will go towards the principal. Neither option B nor option D matches this result.
So neither of the given options, B. \$[/tex]500.00 or D. \$343.68, is correct for the principal portion of the first payment.
