# Word Problems/Real Estate

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Question
Some friends are urging me to chip in with them to buy a vacant parcel of land on the outskirts of our city. A one-fourth interest would cost me \$10,000. Total annual expenses on the property are \$2,200. When the property is sold, assume that I will have to pay a real estate commission of 10% of the selling price and that income taxes on profit will be 15% of the profit. If the property is sold after 3 years, how much will it have to sell for so that I can reap an average annual net return of 10% on my \$10,000? Please explain how you get the answer.

Answer
Let x = selling price of land.

Since \$10,000 represents a one-fourth interest, the purchase price of of the land is \$40,000.
capital gain = x - 40,000
15% capital gains tax = 0.15(x - 40,000) = 0.15x - 6,000
10% realtor commission = 0.10x
other expenses = (3 years)(\$2,200/year) = \$6,600
net return = gain - tax - commission - other
= (x - 40,000) - (0.15x - 6,000) - (0.10x) - (6,600)
= 0.75x - 40,600

(3 years)(10% of \$10,000 per year) = \$3,000
You want a net return of \$3,000. Since you have a one-fourth interest, the target return is \$12,000
0.75x - 40,600 = 12,00
x = \$70,133⅓
If the property sells for \$70,133.33, your share of the return will be \$3,000.

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#### Janet Yang

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Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

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