A broker associate is asked to list a property valuing $95 per square foot and 5% commission. What should the listing price be?

To determine the correct listing price based on the property valuing $95 per square foot and a commission rate of 5%, it’s essential to first understand how to derive the listing price from the sale price.

Given that the broker is entitled to a 5% commission, the listing price must include this commission. The formula to calculate the sale price where the commission is factored in can be expressed as:

Sale Price = Listing Price - (Commission Rate × Listing Price)

This can be rearranged to:

Sale Price = Listing Price × (1 - Commission Rate)

Substituting in the commission rate:

Sale Price = Listing Price × (1 - 0.05)

Sale Price = Listing Price × 0.95

To find the listing price when we know the sale price per square foot is $95, we need to first determine the region of interest—the total sale price based on the desired price per square foot. However, since we don't have the total square footage provided in this question, we instead focus directly on the known outcome based on commission.

To calculate the listing price per square foot, reconciling with the formula leads to realizing that for a sale price of $95 per square foot, the listing price must account for