Real Estate Math Practice Test Questions And Answers

Explanation
The closing cost of two and one half discount points on a $184,000 property with a 75% loan to value ratio can be calculated as follows:
First, calculate the loan amount by multiplying the property value by the loan to value ratio: $184,000 * 0.75 = $138,000.
Next, calculate the discount points by multiplying the loan amount by the percentage of discount points: $138,000 * 2.5% = $3,450.
Therefore, the closing cost would equal $3,450.

Explanation
To calculate the monthly tax, we need to multiply the assessed value of the property ($5,200) by the tax rate (84 mills). Since 1 mill is equal to 0.001, we can convert the tax rate to 0.084. Multiplying $5,200 by 0.084 gives us $436.80. However, the question asks for the monthly tax, so we divide $436.80 by 12 to get $36.40. Therefore, the correct answer is $36.40.

Explanation
To calculate the seller's proportionate share of the unpaid tax at settlement, you need to determine how much of the tax the seller owes for the portion of the year they owned the home.

1. Calculate the number of days the seller owned the home in the tax year. From January 1 to August 15, there are 228 days (since 2022 is not a leap year).

2. Calculate the daily tax amount: $2,640 ÷ 365 days = $7.23 per day (approximately).

3. Calculate the tax owed by the seller for the period they owned the home:
   $7.23 per day × 227 days = $1,641.21 (approximately).

So, the seller's proportionate share of the unpaid tax at settlement would be approximately $1,641.21.

Explanation
The annual rent can be calculated by multiplying the square footage of the store by the rent per square foot and adding the percentage of the gross business sales. The square footage of the store is 41' x 86' = 3,526 square feet. The rent per square foot is $25. The gross business sales in excess of $135,000 is $414,000 - $135,000 = $279,000. The percentage of the gross business sales is 5.5%. Therefore, the additional rent from the gross business sales is $279,000 * 0.055 = $15,345. The total annual rent is $3,526 * $25 + $15,345 = $103,495.

Explanation
If Bob received $3,150 as his 25% of the total commission, we can calculate the total commission by dividing his amount by the percentage. So, $3,150 divided by 25% gives us $12,600. Now, to find the rate of the total commission, we divide the total commission by the selling price of the property ($90,000) and multiply by 100 to get the percentage. Therefore, the rate of the total commission is (12600/90000) * 100 = 14%.

Explanation
To calculate the number of acres in the farmer's field, we need to convert the measurements from miles to acres. One acre is equal to 43,560 square feet. Since the field is one-quarter of a mile by one-half of a mile, we can multiply these dimensions to get the area in square miles, which is 0.25 * 0.5 = 0.125 square miles. To convert this to acres, we multiply by the conversion factor of 640 (the number of acres in one square mile), so 0.125 * 640 = 80 acres. Therefore, the field contains 80 acres.

Explanation
Income from the first three units: 3 units * $775 per unit per month = $2,325 per month
Income from the remaining two units: 2 units * $935 per unit per week * 4 weeks in a month = $7,480 per month
Total Monthly Income: $2,325 + $7,480 = $9,805 per month
Total Quarterly Income: $9,805 per month * 3 months in a quarter = $29,415 per quarter
Now, let's calculate the annual income by multiplying the quarterly income by 4 (since there are 4 quarters in a year):
Total Annual Income: $29,415 per quarter * 4 quarters = $117,660 per year
Now, we can calculate the net annual income by subtracting the total property expenses:
Net Annual Income: $117,660 per year - $3,240 per quarter * 4 quarters = $117,660 per year - $12,960 per year = $104,700 per year
So, the net annual income for Sally Thomas's rental property is $104,700 per year.

Explanation
Lynn Applegate bought a property for $120,000 and sold it for $145,000. She paid a broker's commission of 7% of the selling price, which is $145,000 x 0.07 = $10,150. Her total expenses for the sale are the purchase price plus the broker's commission, which is $120,000 + $10,150 = $130,150. Her profit is the selling price minus the total expenses, which is $145,000 - $130,150 = $14,850. To find the rate of profit, we divide the profit by the purchase price and multiply by 100: ($14,850 / $120,000) x 100 = 12.375%. Therefore, her rate of profit is 12.375%.

Explanation
In this scenario, the monthly payment of $950 is divided into two parts: principal and interest. The interest rate is 8.5% annually, which means that the monthly interest rate is 8.5% divided by 12 months. To calculate the interest portion of the payment, we multiply the outstanding principal balance ($100,000) by the monthly interest rate. The remaining amount of the monthly payment is applied towards the principal. Therefore, the first month's payment towards the principal is $950 - (monthly interest rate * $100,000), which equals $950 - ($100,000 * (8.5%/12)). Simplifying this calculation gives us $950 - $708.33, which equals $241.67.

Explanation
To determine the value of a building based on its monthly net income and an annual rate of return, you can use the formula for the present value of an income-producing asset. Here's how to calculate it:
Convert the annual rate of return to a monthly rate. Since there are 12 months in a year, divide the annual rate by 12:
Monthly Rate = Annual Rate / 12 Monthly Rate = 0.14 / 12 Monthly Rate ≈ 0.01167 (rounded to 5 decimal places)
Use the monthly net income and the monthly rate to calculate the present value (PV):
PV = Monthly Net Income / Monthly Rate PV = $825 / 0.01167 PV ≈ $70,741.95
So, the value of the building, based on a monthly net income of $825 and a 14% annual rate of return, is approximately $70,741.95.

Explanation
To find the price at which the property must sell, we need to determine the original price before the commission was deducted. Since the commission is 6%, we can set up the equation: original price - 6% of original price = $141,000. Simplifying this equation, we get 94% of the original price = $141,000. Dividing both sides by 94% (or multiplying by 100/94), we find that the original price is $149,460. Therefore, the property must sell at this price in order for the seller to receive $141,000 after paying the commission.

Explanation
The subdivision contains a total of 48 acres, and 12.5% of the land is used for roads. Therefore, the usable land for lots is 87.5% of 48 acres, which is 42 acres. Since each lot measures one acre, there will be 42 usable lots in total. The subdivider needs to earn $1,470,000 from the sale of these lots to make the desired profit. Dividing $1,470,000 by 42 gives us the amount the subdivider needs to charge per usable lot, which is $35,000.

Explanation
The first month's interest payment on a loan is $217. To find the amount of the loan, we need to determine the annual interest payment. The annual interest rate is ten and one-half percent, which can be written as 10.5%. To calculate the annual interest payment, we can use the formula: Annual Interest Payment = Loan Amount * Annual Interest Rate. Let's assume the loan amount is x. Therefore, the annual interest payment is 0.105 * x. Since the first month's interest payment is $217, we can set up the equation: 0.105 * x / 12 = $217. Solving for x, we find that the loan amount is $24,800.

Explanation
The loan-to-value ratio is calculated by dividing the mortgage amount by the appraised value of the property and multiplying by 100. In this case, the mortgage amount is $149,760 and the appraised value is $192,000. Dividing $149,760 by $192,000 and multiplying by 100 gives a loan-to-value ratio of approximately 78%.

Explanation
The second month's interest on a $50,000 amortized loan with a 10% annual rate of interest and a level monthly loan payment of $439 can be calculated using the formula: Interest = Principal * Monthly Interest Rate.

The monthly interest rate can be calculated by dividing the annual interest rate by 12 (number of months in a year). So, the monthly interest rate is 10% / 12 = 0.00833.

The principal amount for the second month can be calculated by subtracting the principal amount paid in the first month from the initial loan amount. The principal amount paid in the first month can be calculated by subtracting the interest paid in the first month from the monthly loan payment.

Using these calculations, the second month's interest can be determined to be $416.48.

Explanation
The county-appraised market value of the property is $204,000. The county rate of assessment is 5%, which means that the assessed value of the property is $204,000 * 0.05 = $10,200.

The tax rate for the county institution tax is thirty-four and one-quarter mills, which is equal to 0.03425. The tax amount for the county institution tax is $10,200 * 0.03425 = $349.35.

The tax rate for the borough tax is twenty-nine and one-half mills, which is equal to 0.0295. The tax amount for the borough tax is $10,200 * 0.0295 = $300.90.

Therefore, the total annual tax on the property is $349.35 + $300.90 = $650.25.

Explanation
The listing broker would have earned a commission of 6% on the original listing price. Since the sale price represents a 12% decline from the original listing price, the original listing price can be calculated by dividing the sale price by 0.88 (100% - 12%). Therefore, the original listing price is $165,000 / 0.88 = $187,500. The listing broker's commission on this price would be 6% of $187,500, which is $11,250.

Explanation
To calculate the minimum listing price, we need to divide the desired net amount ($250,000) by the percentage of the commission (5%). This calculation gives us $5,000,000. Therefore, the minimum listing price would be $5,000,000. However, since this amount is not among the given options, we need to choose the closest option. Among the given options, the closest amount to $5,000,000 is $262,500.

Explanation
The sales agent receives a 60% split of the commission, which is 3% of the sale price of $220,000. To calculate the sales agent's earnings, we multiply the sale price by the commission rate and then multiply that by the agent's split percentage. So, $220,000 * 0.03 * 0.6 = $3,960.