- Identify the relationship: \(\text{Property Tax} = \text{Tax Rate} \times \text{Assessed Value}\).
- Set up the equation: \(3164.45 = 0.056 \times V\).
- Solve for \(V\): \(V = \frac{3164.45}{0.056} = 56508.0357\dots\).
- Match the result to the provided options, which gives \(\boxed{c}\).
Explanation
- Problem Analysis and Modeling
The problem asks for the assessed value \(V\) of a property, given a known annual property tax rate and the total tax paid annually. We are provided with:
- Property tax rate: \(0.056\)
- Annual property tax: \(\$3,164.45\)
The relationship between these variables is defined by the formula:
\[\text{Property Tax} = \text{Tax Rate} \times \text{Assessed Value}\]
Substituting the known values, we have:
\[\$3,164.45 = 0.056 \times V\]
- Calculation and Selection of Answer
To find the assessed value \(V\), we rearrange the equation:
\[V = \frac{3,164.45}{0.056}\]
Performing the division, we obtain:
\[V \approx 56,508.0357\]
Rounding to the nearest whole dollar as implied by the options, the assessed value is \(\$56,508\). Comparing this result to the choices provided:
A\(\$177,209\)
B\(\$21,265\)
C\(\$56,508\)
D\(\$48,684\)
The calculated value aligns with option c.
Examples
Property tax is a common financial obligation for homeowners. Understanding how to calculate your property's assessed value from the tax rate and total tax payment is useful for budgeting and verifying property assessment statements. For instance, if you own a home and are reviewing your annual tax bill, you can calculate the total assessment of your property yourself to ensure that the tax authorities have correctly valued your home, which is a foundational aspect of personal financial management.