Question

A real estate agent agrees to sell an apartment complex according to the following commission schedule: $40,000 plus 25% of the selling price in excess of $700,000. Assuming that the complex will sell at some price between $700,000 and $1,000,000 inclusive, over what range does the agent's commission vary? How does the commission vary as a percent of the selling price?

Answer 1

The real estate agent's commission varies from $40,000 to $115,000 for selling prices between $700,000 and $1,000,000. The commission as a percent of the selling price ranges from approximately 5.71% to 11.5% as the selling price increases within the given range.

Step-by-step explanation:

The question asks for the calculation of the range over which a real estate agent's commission will vary given a specific commission schedule. The agent gets $40,000 plus 25% of the selling price over $700,000. To find the range of commission, we consider the minimum and maximum possible selling prices mentioned, which are $700,000 and $1,000,000.

• At a $700,000 selling price, the commission is simply $40,000 since there's no excess over $700,000.
• At a $1,000,000 selling price, the commission is $40,000 plus 25% of ($1,000,000 - $700,000), which is $40,000 + 25% of $300,000 = $40,000 + $75,000 = $115,000.

Therefore, the range of the agent's commission varies from $40,000 to $115,000.

To determine how the commission varies as a percent of the selling price, we can calculate the commission percentage for the minimum ($700,000) and maximum ($1,000,000) selling prices.

• At $700,000, the commission is $40,000, which is approximately 5.71% of the selling price.
• At $1,000,000, the commission is $115,000, which is 11.5% of the selling price.

As the selling price increases from $700,000 to $1,000,000, the commission as a percent of the selling price increases from about 5.71% to 11.5%.