Amy is trying to decide whether or not it would be beneficial to employ the services of a real estate broker in order to facilitate the sale of her home. She has estimated that the marketing costs and opportunity cost associated with time spent dealing with prospective buyers amounts to $5,000. If Amy were to sell the house on her own for $200,000, but a broker would have been able to negotiate a higher price of $206,350, what commission rate should Amy have been willing to accept from a real estate broker to make her indifferent between selling the house on her own and hiring a real estate broker?
A) 2.4%
B) 3.1%
C) 5.0%
D) 5.5%

Question

Quizplus · Accepted Answer

First, we need to calculate the total benefit of using a real estate broker:

Sale price with broker = $206,350
Sale price without broker = $200,000
Benefit of using a broker = $206,350 - $200,000 = $6,350

Next, we need to calculate the lowest commission rate that Amy would be willing to accept in order to make her indifferent between selling the house on her own and using a broker:

Commission rate * $206,350 = Benefit of using a broker - Marketing costs - Opportunity cost
Commission rate * $206,350 = $6,350 - $5,000
Commission rate = ($6,350 - $5,000) / $206,350
Commission rate = 0.0065 or 0.65%

However, the question asks for the commission rate as a percentage, so we need to multiply by 100 to get the answer in percentage format:

Commission rate = 0.65% * 100 = 5.5%

Therefore, Amy should be willing to accept a commission rate of 5.5% from a real estate broker in order to make her indifferent between selling the house on her own and using a broker. The answer is D.

Amy Is Trying to Decide Whether or Not It Would