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A first-time home buyer is given the choice of two loans:

\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{ Loan A } & \multicolumn{1}{c|}{ Loan B } \\
\hline
[tex]$\$[/tex]390,000[tex]$ & $[/tex]\[tex]$390,000$[/tex] \\
15-year fixed & 15-year fixed \\
4 discount points & 0 discount points \\
[tex]$M=\$[/tex]3,509.71[tex]$ & $[/tex]M=\[tex]$3,659.86$[/tex] \\
\hline
\end{tabular}

How much does the home buyer save in total by choosing Loan A?

A. [tex]$\$[/tex]27,027.00[tex]$
B. $[/tex]\[tex]$11,427.00$[/tex]
C. [tex]$\$[/tex]26,351.02[tex]$
D. $[/tex]\[tex]$42,627.05$[/tex]



Answer :

GinnyAnswer
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: \[ \boxed{\$[/tex]27,027.00}
\]

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