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
B) $255,000
The lot area is 150 × 200 = 30,000 square feet. At $8.50 per square foot, the total value is 30,000 × $8.50 = $255,000.
Why This Is the Correct Answer
Option B is correct because it follows the proper two-step calculation process. First, calculate the total area: 150 feet × 200 feet = 30,000 square feet. Second, multiply the area by the per-square-foot value: 30,000 sq ft × $8.50/sq ft = $255,000. This methodology correctly applies the unit rate to the total area to determine overall land value.
Why the Other Options Are Wrong
Option A: $225,000
This answer ($225,000) would result from incorrectly calculating either the area or applying the wrong per-square-foot rate, possibly using $7.50 instead of $8.50 per square foot.
Option C: $275,000
This answer ($275,000) suggests an error in calculation, possibly from miscalculating the area or incorrectly applying a rate closer to $9.17 per square foot instead of the given $8.50.
Option D: $297,500
This answer ($297,500) indicates a significant calculation error, possibly from using an incorrect rate of approximately $9.92 per square foot or making an error in area calculation.
A×R=V Formula
Remember 'ARV' - Area × Rate = Value. Think 'All Real Values' start with knowing the area first, then applying the rate.
How to use: When you see any land valuation problem, immediately identify: A (area calculation needed), R (rate per unit given), then multiply for V (total value). Always calculate area first, then apply the rate.
Exam Tip
Double-check your area calculation by ensuring you're multiplying length × width correctly, and verify your final multiplication by estimating (30,000 × $8.50 should be close to 30,000 × $8 = $240,000 plus a bit more).
Common Mistakes to Avoid
- -Forgetting to calculate total area first before applying the rate
- -Mixing up the dimensions or using incorrect area formulas
- -Misplacing decimal points when multiplying large numbers by dollar amounts
Concept Deep Dive
Analysis
This question tests fundamental area calculation and land valuation skills essential for real estate appraisers. It combines basic geometry (calculating rectangular area) with per-unit pricing methodology commonly used in land valuation. The problem requires students to understand that land value is often expressed as a rate per square foot, and total value is determined by multiplying the total area by this unit rate. This type of calculation is foundational to the sales comparison approach and land valuation methods used throughout appraisal practice.
Background Knowledge
Appraisers must be proficient in calculating areas of various geometric shapes, as land parcels come in different configurations. Understanding per-unit pricing is crucial since land values are commonly expressed as rates per square foot, per acre, or per front foot depending on the property type and local market practices.
Real-World Application
Appraisers regularly use per-square-foot land values when applying the sales comparison approach, comparing similar vacant land sales to value a subject property, or when performing highest and best use analysis to determine if improvements add value beyond the underlying land.
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