In this module, we learned about real estate agents$/$brokers and simple calculations relating to commissions. Please answer these real world questions.

$1-$ Madison 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 $$5,000.$ If Madison were to sell the house on her own for $$200,000,$ but a broker would have been able to negotiate a higher price of $$206,350,$ what commission rate should Madison 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?

$2-$ Julio has hired a real estate broker to help facilitate the sale of his home. If the broker requires a commission of $6\%,$ how much will Julio clear from the sale $($aftier the commission has been paid$)$ if he is able to sell his house for $$478,723?($Assume that Julio has already paid off his mortgage$)$

$3-$ Suppose you are interested in selling your home and would like to clear a net value of $$300,000.$ If you have agreed to pay your broker a commission of $5\mathrm{.}5\%($no matter who ultimately is responsible for finding the buyer$),$ what price must you sell the home for in order to meet your net profit $($rounded to the nearest dollar$)?$

Submission Guidelines:

Use Excel to complete and show all work and calculations.