Final answer:
To find the selling price that nets the owner $45,000 after paying a mortgage balance of $68,000 and a broker's commission of 7%, you calculate the total needed before commission (mortgage balance + desired net amount) and divide by (1 - commission rate). The correct calculation gives a selling price of $121,505.38, not in the options, so we select the closest option, which is b) $119,700.
Step-by-step explanation:
To determine the selling price of a house that would net the owner $45,000 after paying off a mortgage balance and broker commission, we first need to determine the total amount that needs to be covered, including the commission. The broker's commission is 7% of the selling price, so we can represent the selling price as 100% - 7%, which is 93% or 0.93 of the selling price.
Now, let's add up all the costs that need to be covered:
- Mortgage balance: $68,000
- Desired net amount: $45,000
The total amount to be covered is $68,000 (mortgage) + $45,000 (net amount) = $113,000.
So we have 0.93 (selling price) = $113,000 and therefore, the selling price is $113,000 / 0.93 = $121,505.38. Since this is not one of the options, let us check our calculation for a mistake. If we recalculate, knowing that the commission is subtracted after the mortgage, we get:
Net amount to owner + Mortgage = Net Selling Price
Therefore, $45,000 + $68,000 = $113,000
To find the total selling price including commission:
Total Selling Price = Net Selling Price / (1 - Commission Rate)
Total Selling Price = $113,000 / (1 - 0.07) = $113,000 / 0.93 = $121,505.38. Once again, since this is not one of the options, we need to recount for any mistakes.
Upon revisiting the calculation, we recognize that the correct approach involves considering the broker's commission based on the final selling price. The selling price minus 7% of it should equal the sum of the mortgage balance and the net amount the owner desires:
Selling Price - 0.07(Selling Price) = $68,000 + $45,000
Selling Price (1 - 0.07) = $113,000
Selling Price * 0.93 = $113,000
Selling Price = $113,000 / 0.93
Selling Price = $121,505.38
However, this calculated selling price is not among the given options. We need to round to the nearest option provided, realizing that our original calculation was correct and that the original list of options did not contain the exact correct answer, we can see that option b) $119,700 is the closest to our calculated selling price, so this should be selected as the correct answer to the question.