We have been given that Broker P charges a commission of $8.50 for every ten shares of stock, and Broker Q charges a fee of $65.00 for every thousand dollars bought or sold.
Let us find commission of each broker to buy 500 shares.
[tex]\text{Broker P will charge}=\frac{8.50}{10} \times 500[/tex]
[tex]\text{Broker P will charge}=8.50 \times 50[/tex]
[tex]\text{Broker P will charge}=425[/tex]
Broker P will charge $ 425 for 500 shares.
Let us find commission for broker Q.
[tex]\text{Cost of buying Ergar Appliances share}=18.75 \times 500[/tex]
[tex]\text{Cost of buying Ergar Appliances share}=9375[/tex]
We are told that Broker Q charges a fee of $65.00 for every thousand dollars bought or sold. 9375 is same as 9.375 thousands.
To find broker Q's commission we will multiply 9.375 by 65.
[tex]\text{Broker Q will charge}=65 \times 9.375[/tex]
[tex]\text{Broker Q will charge}=609.375[/tex]
We can see that broker Q is charging more than broker P. Let us find difference of commissions of both brokers.
[tex]609.375-425=184.375[/tex]
Therefore, Broker P is the better deal by $184.375.
