A property in Arizona sells for $400,000. If the agent earns 3% on the first $100,000 and 2.5% on the remainder, what is the total commission?
Correct Answer
A) $10,500
First $100,000 × 3% = $3,000. Remaining $300,000 × 2.5% = $7,500. Total = $10,500.
Why This Is the Correct Answer
First $100,000 × 3% = $3,000. Remaining $300,000 × 2.5% = $7,500. Total = $10,500.
Why the Other Options Are Wrong
Option B: $10,000
This answer incorrectly applies a flat 2.5% rate to the entire $400,000, ignoring the higher 3% rate on the first $100,000. This mistake fails to account for the tiered commission structure specified in the question.
Option C: $11,500
This answer likely results from adding the two commission percentages (3% + 2.5% = 5.5%) and applying that to the full amount, or incorrectly calculating the remaining amount after the first $100,000.
Option D: $12,000
This answer might come from applying 3% to the full $400,000 or adding the percentages incorrectly. It demonstrates a failure to recognize the tiered nature of the commission structure.
Deep Analysis of This Real Estate Math Question
Commission calculation is a fundamental skill in real estate practice as it directly impacts an agent's income and affects transaction transparency with clients. This question tests your ability to apply tiered commission structures, which are common in real estate. The core concept involves calculating commissions at different rates based on specific price thresholds. To solve this, we break the property value into portions: $100,000 at 3% and the remaining $300,000 at 2.5%. The challenge lies in correctly identifying the threshold and applying the right rate to each portion. Many students struggle with tiered calculations because they either misidentify the threshold rates or fail to properly divide the total sales price. Understanding this concept is crucial not only for exam success but also for advising clients on commission structures and negotiating compensation with brokers.
Background Knowledge for Real Estate Math
Tiered commission structures are common in real estate to balance agent compensation for properties of varying values. They often provide higher rates for the initial portion of the sale price to ensure fair compensation for smaller properties, while reducing rates for higher portions to remain competitive in the market. This structure aligns with the principle that smaller properties typically represent more work relative to their value compared to luxury properties. In Arizona, as in most states, commission rates are negotiable between brokers and determined through market competition, not fixed by regulation.
Memory Technique
visualPicture a staircase with two steps. The first step (first $100,000) is higher (3%) and the second step (remaining amount) is slightly lower (2.5%). Imagine climbing these steps while calculating the commission for each portion.
When you see tiered commission questions, visualize the staircase to remind yourself to calculate each portion separately at its respective rate.
Exam Tip for Real Estate Math
For tiered commission questions, always identify the thresholds and rates first, then calculate each portion separately before adding them together. Double-check that you've correctly divided the total amount according to the specified thresholds.
Real World Application in Real Estate Math
Sarah, a Phoenix real estate agent, lists a home for $385,000 with her broker. They agree on a commission split where Sarah receives 3% on the first $100,000 and 2.5% on the remainder. When the property sells at $400,000, Sarah needs to calculate her commission. She breaks down the calculation: $3,000 from the first $100,000 and $7,500 from the remaining $300,000, totaling $10,500. This helps her accurately project her earnings and provide transparency to her broker.
Common Mistakes to Avoid on Real Estate Math Questions
- •Applying a single commission rate to the entire property value instead of recognizing the tiered structure
- •Incorrectly calculating the remaining amount after the first threshold ($400,000 - $100,000 = $300,000, not $200,000)
- •Adding the commission percentages together and applying the sum to the total value
Related Topics & Key Terms
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