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You have just been approved for a 30-year [tex]5.5\%[/tex] fixed home mortgage. The monthly payment that you qualify for is [tex]\$532.10[/tex]. Use the table provided to determine the price of a home that can be purchased. Round your answer to the nearest cent.

Monthly Payments per [tex]\$1000[/tex] of Mortgage
\begin{tabular}{|c|c|c|c|c|}
\hline
\begin{tabular}{c}
Interest \\
Rate (\%)
\end{tabular} & 10 Years & 20 Years & 30 Years & 40 Years \\
\hline
5.0 & 10.61 & 6.60 & 5.37 & 4.83 \\
\hline
5.5 & 10.86 & 6.88 & 5.68 & 5.16 \\
\hline
6.0 & 11.11 & 7.17 & 6.00 & 5.51 \\
\hline
6.5 & 11.36 & 7.46 & 6.33 & 5.86 \\
\hline
\end{tabular}

a. [tex]\$98,258.68[/tex]
b. [tex]\$103,879.65[/tex]
c. [tex]\[tex]$104,120.32[/tex]
d. [tex]\$[/tex]93,679.60[/tex]

Please select the best answer from the choices provided.


Sagot :

Let's solve this step-by-step:

1. Identify the Given Information:
- Monthly payment: [tex]\(\$532.10\)[/tex]
- Interest rate: [tex]\(5.5\%\)[/tex]
- Duration: 30 years
- Monthly payment per [tex]\(\$1000\)[/tex] mortgage for 30 years at [tex]\(5.5\%\)[/tex]: [tex]\( \$5.68\)[/tex]

2. Set Up the Formula:
We use the formula that relates the monthly payment to the price of the home:
[tex]\[ \text{Monthly Payment} = \left( \frac{\text{Price of the Home}}{1000} \right) \times \text{Monthly Payment per $1000$} \][/tex]
Rearrange the formula to solve for the price of the home:
[tex]\[ \text{Price of the Home} = \frac{\text{Monthly Payment} \times 1000}{\text{Monthly Payment per $1000$}} \][/tex]

3. Substitute the Given Values:
[tex]\[ \text{Price of the Home} = \frac{532.10 \times 1000}{5.68} \][/tex]

4. Calculate:
[tex]\[ \text{Price of the Home} = \frac{532100}{5.68} \approx 93679.57746478873 \][/tex]

5. Round the Answer:
[tex]\[ \text{Rounded Price of the Home} = 93679.58 \][/tex]

6. Compare with the Given Options:
The given options are:
- [tex]\(\$ 98,258.68\)[/tex]
- [tex]\(\$ 104,120.32\)[/tex]
- [tex]\(\$ 103,879.65\)[/tex]
- [tex]\(\$ 93,679.60\)[/tex]

Among these, the closest option to [tex]\(\$ 93679.58\)[/tex] is [tex]\(\$ 93,679.60\)[/tex].

Therefore, the best answer from the choices provided is:

d. \$ 93,679.60
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