Let's analyze the given information step-by-step to find out how much the home buyer saves by choosing Loan A over Loan B.
1. Monthly Payment for Loan A:
- Loan A has a monthly payment ([tex]\( M \)[/tex]) of \[tex]$3,509.71.
2. Monthly Payment for Loan B:
- Loan B has a monthly payment (\( M \)) of \$[/tex]3,659.86.
3. Loan Term:
- Both loans have a term of 15 years.
4. Convert Years to Months:
- There are 12 months in a year.
- Therefore, the loan term in months is [tex]\( 15 \)[/tex] years [tex]\(\times 12\)[/tex] months/year = 180 months.
5. Compute Total Payments:
- For Loan A: The total payment over the loan term is
[tex]\[
\$3,509.71 \, \text{per month} \times 180 \, \text{months} = \$631,747.80
\][/tex]
- For Loan B: The total payment over the loan term is
[tex]\[
\$3,659.86 \, \text{per month} \times 180 \, \text{months} = \$658,774.80
\][/tex]
6. Calculate Savings by Choosing Loan A:
- The total amount saved by choosing Loan A over Loan B is the difference between the total payments for each loan:
[tex]\[
\$658,774.80 - \$631,747.80 = \$27,027.00
\][/tex]
Therefore, the home buyer saves [tex]$\$[/tex]27,027.00[tex]$ in total by choosing Loan A over Loan B.
The correct answer is:
\[
\boxed{\$[/tex]27,027.00}
\]
