To determine how much of the first mortgage payment will go towards the principal, we need to understand how mortgage payments are typically structured. Each mortgage payment consists of two parts: the interest portion and the principal portion.
Let's walk through the steps to find out how much of the first payment (which is \[tex]$532) goes toward the principal.
1. Calculate the Monthly Interest Rate:
The annual interest rate is 3%, so we need the monthly interest rate. The monthly interest rate is calculated by dividing the annual rate by 12.
\[
\text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12}
\]
Given that the annual interest rate is 3%, or 0.03 in decimal form, the monthly interest rate is:
\[
\text{Monthly Interest Rate} = \frac{0.03}{12} = 0.0025
\]
2. Calculate the Interest Portion of the First Payment:
The interest portion of the payment is determined by applying the monthly interest rate to the principal balance.
\[
\text{Interest First Payment} = \text{Principal} \times \text{Monthly Interest Rate}
\]
With a principal of \$[/tex]150,000, the interest portion of the first payment is:
[tex]\[
\text{Interest First Payment} = 150,000 \times 0.0025 = 375.00
\][/tex]
3. Determine the Principal Portion of the First Payment:
The principal portion is the amount remaining from the total monthly payment after the interest has been paid.
[tex]\[
\text{Principal First Payment} = \text{Monthly Payment} - \text{Interest First Payment}
\][/tex]
Given a monthly payment of \[tex]$532 and an interest first payment of \$[/tex]375:
[tex]\[
\text{Principal First Payment} = 532 - 375 = 157.00
\][/tex]
Thus, the amount of the first payment that will go towards the principal is [tex]\( \text{\$157.00} \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{A.\ \$157.00}
\][/tex]
