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Math

QuestionWhat sales price is needed for a 400,000400,000 property to achieve a 15%15\% net gain after a 6%6\% broker commission?

Studdy Solution

STEP 1

Assumptions1. The original cost of the property is \$400,000. The owner wants a net15% appreciation on the original cost3. The selling broker gets a6% commission on the sales price

STEP 2

First, we need to find the amount of appreciation the owner wants. This can be done by multiplying the original cost by the appreciation rate.
Appreciation=Original costtimesAppreciation rateAppreciation = Original\, cost \\times Appreciation\, rate

STEP 3

Now, plug in the given values for the original cost and appreciation rate to calculate the appreciation.
Appreciation=$400,000times15%Appreciation = \$400,000 \\times15\%

STEP 4

Convert the percentage to a decimal value.
15%=0.1515\% =0.15Appreciation=$400,000times0.15Appreciation = \$400,000 \\times0.15

STEP 5

Calculate the appreciation amount.
Appreciation=$400,000times0.15=$60,000Appreciation = \$400,000 \\times0.15 = \$60,000

STEP 6

Now that we have the appreciation amount, we can find the total amount the owner wants to receive. This includes both the original cost and the appreciation.
Total amount=Original cost+AppreciationTotal\, amount = Original\, cost + Appreciation

STEP 7

Plug in the values for the original cost and the appreciation to calculate the total amount.
Total amount=$400,000+$60,000Total\, amount = \$400,000 + \$60,000

STEP 8

Calculate the total amount the owner wants to receive.
Total amount=$400,000+$60,000=$460,000Total\, amount = \$400,000 + \$60,000 = \$460,000

STEP 9

Now that we have the total amount the owner wants to receive, we can find the sales price. The sales price is the total amount divided by ( - commission rate).
Sales price=Total amount/(−Commission rate)Sales\, price = Total\, amount / ( - Commission\, rate)

STEP 10

Convert the commission rate to a decimal value.
6%=0.066\% =0.06

STEP 11

Plug in the values for the total amount and the commission rate to calculate the sales price.
Sales price=$460,000/(−0.06)Sales\, price = \$460,000 / ( -0.06)

STEP 12

Calculate the sales price.
Sales price=$460,000/0.94=$489,361.70Sales\, price = \$460,000 /0.94 = \$489,361.70The sales price of the property must be \$489,361.70.

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