Question

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 5.5% (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)?A. $282,540
B. $300,000
C. $316,500
D. $317,460

Answer 1

The correct answer is:

$317,460 (D.)

Step-by-step explanation:

At the end of sales, after deducting the 5.5% commission of broker fee, the amount left as net value = $300,000. It can also be said that the total amount will be $300,000 + 5.5% of the total amount.

Let the price which the home is to be sold be "X"

From the statement above, the equation below can be written:

$300,000 + (5.5% of X) = X

X - (5.5% of X) = $300,000

Note that 5.5% of X = 5.5/100 × X = 0.055X

∴ X - (5.5% of X) = $300,000

= X - 0.055X = 300,000

0.945X = 300,000

X =
`(300,000)/(0.945) = 317,460.31`

= $317,460 (to the nearest dollars)