Final answer:
The homeowner should list the property for at least $529,100.53 to cover the original purchase price of $500,000 plus the 5.5% sales commission in order to break even.
Step-by-step explanation:
To calculate the listing price needed for the homeowner to at least break even after selling the property with the sales agent's commission of 5.5%, we need to account for the commission in the final sale price. First, let's define the original purchase price as P, which is $500,000. The sales commission is represented as C, which is 5.5% or 0.055. To break even, the homeowner needs to recover P plus the sales commission. The equation to calculate the listing price (L) will be:
L = P / (1 - C)
Plugging in the values we have:
L = $500,000 / (1 - 0.055)
L = $500,000 / 0.945
L = $529,100.53
Therefore, the homeowner should list the property for at least $529,100.53 to break even after accounting for the sales commission.