An owner lists her home at a 7% commission rate and wants to net $45,000 after paying the mortgage balnce of $68,000 and the broker's commission. To the nearest dollar, what should the selling price be to net her $45,000?
Ps-0.07Ps = 6,8000 + 45,000.
Solve for Ps, the selling price.
To find the selling price that will allow the owner to net $45,000 after paying the mortgage balance and the broker's commission, we need to perform the following steps:
Step 1: Calculate the broker's commission
The broker's commission is calculated as a percentage of the selling price. In this case, the commission rate is 7%, so we need to determine 7% of the selling price.
Broker's commission = 7% of selling price
Step 2: Determine the remaining amount after paying off the mortgage and the broker's commission
After paying the mortgage balance and the broker's commission, the owner wants to net $45,000. So, we subtract these costs from the selling price.
Remaining amount = Selling price - Mortgage balance - Broker's commission
Step 3: Set up the equation
Now, we can put all the information together and set up the equation:
Remaining amount = $45,000
Selling price - $68,000 - (7% of selling price) = $45,000
Step 4: Solve for the selling price
We can solve the equation to find the selling price that will allow the owner to net $45,000.
Selling price - $68,000 - (0.07 * Selling price) = $45,000
Combine like terms:
0.93 * Selling price = $113,000
Divide both sides by 0.93 to isolate Selling price:
Selling price = $113,000 / 0.93
Using a calculator, the selling price is approximately $121,505 (rounded to the nearest dollar) in order to net the owner $45,000 after paying the mortgage balance and broker's commission.