A rectangular lot measures 150 feet by 200 feet. If the lot is valued at $8.50 per square foot, what is the total land value?
Correct Answer
A) $255,000
First calculate the area: 150 feet × 200 feet = 30,000 square feet. Then multiply by the price per square foot: 30,000 × $8.50 = $255,000.
Why This Is the Correct Answer
Option A is correct because it follows the proper two-step calculation process. First, the area is calculated: 150 feet × 200 feet = 30,000 square feet. Then, this area is multiplied by the per-square-foot value: 30,000 square feet × $8.50 = $255,000. This systematic approach ensures accuracy and follows standard appraisal methodology for land valuation calculations.
Why the Other Options Are Wrong
Option B: $127,500
This represents only half the correct answer ($255,000 ÷ 2 = $127,500), suggesting the test-taker may have made an error in the area calculation or incorrectly divided the final result by 2.
Option C: $30,000
This is only the area in square feet (30,000), indicating the test-taker calculated the area correctly but forgot to multiply by the price per square foot ($8.50).
Option D: $2,975
This extremely low value suggests a fundamental calculation error, possibly confusing the dimensions or making multiple arithmetic mistakes in both area calculation and price multiplication.
Area × Rate = Value (ARV)
Remember 'ARV' - Area × Rate = Value. Always calculate the area first (length × width for rectangles), then multiply by the rate per square foot to get the total value.
How to use: When you see any land valuation problem, immediately think 'ARV' and follow the sequence: 1) Calculate Area (length × width), 2) Apply Rate (price per sq ft), 3) Get Value (total land value).
Exam Tip
Always double-check your area calculation before multiplying by the price per square foot, and verify your final answer makes sense given typical land values in the problem context.
Common Mistakes to Avoid
- -Forgetting to multiply area by price per square foot
- -Calculating perimeter instead of area
- -Making arithmetic errors in multiplication
- -Confusing length and width measurements
- -Using incorrect units or forgetting to convert measurements
Concept Deep Dive
Analysis
This question tests fundamental area calculation and land valuation skills essential for real estate appraisers. It requires understanding how to calculate the area of rectangular parcels and apply per-square-foot pricing to determine total land value. The problem combines basic geometry with real estate mathematics, which forms the foundation for more complex valuation calculations. This type of calculation is frequently encountered in both exam settings and professional practice when determining land values for comparable sales analysis or cost approach valuations.
Background Knowledge
Real estate appraisers must be proficient in calculating areas of various lot shapes, with rectangular lots being the most common and straightforward. Understanding per-square-foot pricing is essential for land valuation, as it's a standard method used in the sales comparison approach and for determining land values in the cost approach.
Real-World Application
Appraisers regularly use this calculation when analyzing comparable land sales, determining site values for the cost approach, or valuing vacant land parcels where recent sales data provides per-square-foot pricing benchmarks.
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