Please help me,math word problems make my brain go crazy.
Some friends are urging you to chip in with them to buy a vacant parcel og land on the outskirts of your city. A one-fourth interest would cost you $10,000.Total annual expenses on the property are $2,200.When the property is sold,assume that you'll have to pay a real estate commission of 10% of the selling price and that the income taxes on any profit will be 15% of the profit.If the property is sold after 3 yrs,how much will it have to sell for so that you can reap an average annual net return of 10% of your $10,000?HELP PLEASE!
To solve this math word problem, we'll break it down into steps.
Step 1: Calculate the total expenses per year for the property.
The problem states that the total annual expenses on the property are $2,200.
Step 2: Calculate your annual expenses for your one-fourth interest.
Since you own a one-fourth interest, you can calculate your annual expenses by dividing the total annual expenses by four:
$2,200 / 4 = $550
Step 3: Calculate the total net income required per year.
To earn an average annual net return of 10% of your $10,000 investment, you'll need to earn $1,000 per year ($10,000 * 10%).
Step 4: Calculate the net income required for your one-fourth interest.
Since you own a one-fourth interest, you can calculate your required net income by dividing the total net income required by four:
$1,000 / 4 = $250
Step 5: Calculate the total net income after subtracting expenses.
To find the selling price needed, you'll need to determine the net income after subtracting the expenses. Subtract the annual expenses for your one-fourth interest from the required net income:
$250 - $550 = -$300
Step 6: Calculate the profit needed to achieve a positive net income.
Since the net income after expenses is currently negative, you'll need to calculate the required profit to achieve a positive net income. To do this, set up the equation:
Profit * (1 - 15%) - 10% of selling price = -$300
Step 7: Simplify and solve the equation for the profit.
Profit * 0.85 - 0.10 * Selling Price = -$300
Since the problem states that the property will be sold after 3 years, multiply the profit by 3 to account for the 3-year period:
3 * Profit * 0.85 - 0.10 * Selling Price = -$300
Simplifying further:
2.55 * Profit - 0.10 * Selling Price = -$300
Step 8: Solve for the selling price.
To solve for the selling price, rearrange the equation:
0.10 * Selling Price = 2.55 * Profit + $300
Simplify the equation further:
Selling Price = (2.55 * Profit + $300) / 0.10
Step 9: Calculate the required profit.
To calculate the required profit, divide the required net income by the number of years the property will be held:
Profit = $250 / 3 = $83.33 (approximately)
Step 10: Calculate the selling price.
Plug the value of Profit into the equation from step 8:
Selling Price = (2.55 * $83.33 + $300) / 0.10
Selling Price = ($212.42 + $300) / 0.10
Selling Price = $512.42 / 0.10
Selling Price ≈ $5,124.20
Therefore, the property will have to sell for approximately $5,124.20 in order for you to reap an average annual net return of 10% of your $10,000 investment after 3 years.