A jurisdiction assesses property at exactly 85% of current market value, with no other assessment adjustments or exemptions. If a property's assessed value is $180,000, what is its market value, to the nearest dollar?
Correct Answer
D) $211,765
Market figure=$180,000/0.85=$211,764.7059; nearest whole dollar=$211,765. This is the numerical result under the stated definitions, not an automatic market-condition or property-value conclusion. Common errors: multiplying by 0.85 instead of dividing gives $153,000; adding 15% instead of dividing by 0.85 gives $207,000; reporting the difference instead of the market figure gives $31,765.
Why This Is the Correct Answer
Option D is correct because assessed value = 0.85 x market value, so market value = $180,000 / 0.85 = $211,764.71, rounded to $211,765. Dividing by the ratio reverses the relationship. This example does not describe any state's assessment law.
Why the Other Options Are Wrong
Option A: $31,765
Option A, $31,765, reports the difference instead of the market figure: $180,000 / 0.85 - $180,000 = $31,765. The question asks for the market figure itself, which is $180,000 / 0.85 = $211,765.
Option B: $153,000
Option B, $153,000, comes from multiplying by 0.85 instead of dividing: $180,000 x 0.85 = $153,000. Since assessed value is 85% of market value, the market figure must be larger: $180,000 / 0.85 = $211,765.
Option C: $207,000
Option C, $207,000, comes from adding 15% instead of dividing by 0.85: $180,000 x 1.15 = $207,000. Adding 15% of the assessed value is not the same as dividing by 0.85; the correct result is $180,000 / 0.85 = $211,765.
Part over percent gives whole
If the assessed value is a part of market value, divide the part by its percentage to get the whole.
How to use: Use this whenever you know a value and the percentage of the whole it represents.
Exam Tip
When a known figure is a percentage of the unknown, divide by that percentage; the answer must be larger than the known figure if the percentage is under 100%.
Common Mistakes to Avoid
- -Multiplying by the assessment ratio instead of dividing
- -Adding the complement percentage instead of dividing
- -Reporting the difference rather than the market figure
Concept Deep Dive
Analysis
This question tests inverting an assessment ratio. If assessed value equals 85% of market value, then market value equals assessed value divided by 0.85. So $180,000 / 0.85 = $211,764.71, which rounds to $211,765.
Background Knowledge
An assessment ratio is the fractional relationship of an assessed value to the market value of the property. When the ratio is known, market value can be estimated by dividing assessed value by the ratio. Appraisers treat assessed values with caution, since actual assessment practices vary and may not track market value closely.
Real-World Application
An appraiser is told that a jurisdiction assesses at a stated 85% ratio and that a home's assessed value is $180,000. The appraiser divides by 0.85 to get about $211,765, then notes that this is only an indicator and checks it against actual sales.
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