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
