Real Estate Math Practice Test Questions And Answers

1. A property is appraised at the request of a lender in order to provide a mortgage. The property value is determined to be $192,000. The lender provides a mortgage in the amount of $149,760. What is the loan-to-value ratio?

78%

86%

88%

128%

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 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%.

2. If Bob received $3,150 as his 25% of the total commission on the sale of a $90,000 property, then what is the rate of the total commission?

6%

7%

14%

15%

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

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%.

3. A broker shares the commission that is earned on the sale of real estate with a salesperson in a ratio of 3:2, respectively. If the salesperson sells a property for $148,000, on which the office commissions are 5% of the sale price, then how much more would the broker earn than the salesperson?

$1,576

$1,480

$1,960

$7,400

First, let's calculate the total commission earned on the sale:

Total commission = 5% of $148,000 Total commission = 0.05 * $148,000 Total commission = $7,400

Now, let's find out how much of this commission each earns based on the ratio:

Broker's share = 3/5 * $7,400 Broker's share = $4,440

Salesperson's share = 2/5 * $7,400 Salesperson's share = $2,960

Now, let's find out how much more the broker earns than the salesperson:

Difference = Broker's share - Salesperson's share Difference = $4,440 - $2,960 Difference = $1,480

Therefore, the broker would earn $1,480 more than the salesperson.

Explanation

First, let's calculate the total commission earned on the sale:

Total commission = 5% of $148,000 Total commission = 0.05 * $148,000 Total commission = $7,400

Now, let's find out how much of this commission each earns based on the ratio:

Broker's share = 3/5 * $7,400 Broker's share = $4,440

Salesperson's share = 2/5 * $7,400 Salesperson's share = $2,960

Now, let's find out how much more the broker earns than the salesperson:

Difference = Broker's share - Salesperson's share Difference = $4,440 - $2,960 Difference = $1,480

Therefore, the broker would earn $1,480 more than the salesperson.

4. In 2022, the calendar year's taxes on a home is $2,640. If the owner sells the home on August 15, 2022, what would be the seller's proportionate share of the unpaid tax at settlement?

$650

$1,641.21.

$187

$1,870

To calculate the seller's proportionate share of the unpaid tax at settlement, we need to determine how much of the year's taxes the seller is responsible for up to the date of the sale on August 15, 2022.

First, we find the number of days from January 1 to August 15, 2022:

From January 1 to July 31: 31 (days in January) + 28 (days in February) + 31 (days in March) + 30 (days in April) + 31 (days in May) + 30 (days in June) + 31 (days in July) = 212 days

From August 1 to August 15: 15 days Total days = 212 + 15 = 227 days

Next, we find the proportionate share of the taxes for the period from January 1 to August 15: Proportionate share = (Number of days / Total days in the year) * Total taxes for the year Proportionate share = (227 / 365) * $2,640 Proportionate share ≈ $1,641.21

So, the correct answer is $1,641.21.

Explanation

To calculate the seller's proportionate share of the unpaid tax at settlement, we need to determine how much of the year's taxes the seller is responsible for up to the date of the sale on August 15, 2022.

First, we find the number of days from January 1 to August 15, 2022:

From January 1 to July 31: 31 (days in January) + 28 (days in February) + 31 (days in March) + 30 (days in April) + 31 (days in May) + 30 (days in June) + 31 (days in July) = 212 days

From August 1 to August 15: 15 days Total days = 212 + 15 = 227 days

Next, we find the proportionate share of the taxes for the period from January 1 to August 15: Proportionate share = (Number of days / Total days in the year) * Total taxes for the year Proportionate share = (227 / 365) * $2,640 Proportionate share ≈ $1,641.21

So, the correct answer is $1,641.21.

5. The owners of a shopping mall charge satellite store owners an annual rent of $25 per square foot of storage area in addition to 5 and 1/2 % of the gross business sales in excess of $135,000. If the dimensions of the store are 41' x 86' and the owner sells $414,000 worth of sporting goods during the year, what is the annual rent.

$15,345

$88,150

$103,495

$124,305

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

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.

6. If a farmer's field is one-quarter of a mile by one-half of a mile, how many acres does it contain?

80

100

120

160

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

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.

7. Sally Thomas rents the first three of her five rental units at $775 per unit per month and the remaining units at $935 per unit per week. If the total property expenses are $3,240 per quarter, what is the net annual income?

$12,960

$80,640

$112,180

$125,140

To calculate the net annual income, we need to consider the income from the first three rental units and the remaining units separately.

Income from the first three units:

Monthly rent per unit: $775

Number of units: 3

Monthly income from the first three units: $775 * 3 = $2,325

Annual income from the first three units: $2,325 * 12 = $27,900

Income from the remaining two units:

Weekly rent per unit: $935

Number of units: 2

Weekly income from the remaining units: $935 * 2 = $1,870

Annual income from the remaining units: $1,870 * 52 = $97,240

Total annual income:

$27,900 (from the first three units) + $97,240 (from the remaining units) = $125,140

Total annual expenses:

Quarterly expenses: $3,240 * 4 = $12,960

Net annual income:

$125,140 (total annual income) - $12,960 (total annual expenses) = $112,180

Therefore, the net annual income is $112,180.

Explanation

To calculate the net annual income, we need to consider the income from the first three rental units and the remaining units separately.

Income from the first three units:

Monthly rent per unit: $775

Number of units: 3

Monthly income from the first three units: $775 * 3 = $2,325

Annual income from the first three units: $2,325 * 12 = $27,900

Income from the remaining two units:

Weekly rent per unit: $935

Number of units: 2

Weekly income from the remaining units: $935 * 2 = $1,870

Annual income from the remaining units: $1,870 * 52 = $97,240

Total annual income:

$27,900 (from the first three units) + $97,240 (from the remaining units) = $125,140

Total annual expenses:

Quarterly expenses: $3,240 * 4 = $12,960

Net annual income:

$125,140 (total annual income) - $12,960 (total annual expenses) = $112,180

Therefore, the net annual income is $112,180.

8. What is the value of a building that has a monthly net income of $825 and is earning the owner a 14% annual rate of return?

$58,928.95

$70,741.95

$90,514.95

$106,932.95

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 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.

9. A sub-divider needs to earn $1,470,000 from the sale of the usable lots in a subdivision to make the desired profit. The subdivision contains a total of 48 acres. Twelve and one-half percent of the subdivision land is to be used for roads. If each lot measures one acre, then what does the other subdivider need to charge per usable lot to make his desired profit.

$30,625

$35,000

$42,000

$48,625

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 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.

10. A closing cost of two and one half discount points involved in the purchase of a $184,000 property on which there is a mortgage with a 75% loan to value ratio would equal which of the following amounts:

$3,450

$3,540

$4,600

$138,000

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

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.

11. If the first month's interest payment on a loan is $217 and the annual rate of interest is ten and one-half percent, then what is the amount of the loan?

$22,400

$24,200

$28,400

$24,800

To calculate the loan amount based on the first month's interest payment of $217 and an annual interest rate of 10.5%, we annualize the interest payment by multiplying by 12 (months) and then divide by the annual interest rate (converted to a decimal). This reveals the principal amount of the loan to be $24,800.

Explanation

To calculate the loan amount based on the first month's interest payment of $217 and an annual interest rate of 10.5%, we annualize the interest payment by multiplying by 12 (months) and then divide by the annual interest rate (converted to a decimal). This reveals the principal amount of the loan to be $24,800.

12. If a seller needs to receive $141,000 after paying a real estate commission of 6%, at what price must the property sell?

$141,000

$150,000

$153,000

$156,540

To find out the selling price needed for the seller to receive $141,000 after paying a 6% real estate commission, we can set up the equation:

Let x be the selling price.

The seller receives 100% - 6% = 94% of the selling price (since the commission is 6%).

So, 94% of x = $141,000.

To solve for x, we can set up the equation:

0.94x = $141,000.

Dividing both sides by 0.94 to isolate x:

x = $141,000 / 0.94.

x ≈ $150,000.

Therefore, the property must sell for approximately $150,000 for the seller to receive $141,000 after paying a 6% real estate commission.

So, the correct answer is $150,000.

Explanation

To find out the selling price needed for the seller to receive $141,000 after paying a 6% real estate commission, we can set up the equation:

Let x be the selling price.

The seller receives 100% - 6% = 94% of the selling price (since the commission is 6%).

So, 94% of x = $141,000.

To solve for x, we can set up the equation:

0.94x = $141,000.

Dividing both sides by 0.94 to isolate x:

x = $141,000 / 0.94.

x ≈ $150,000.

Therefore, the property must sell for approximately $150,000 for the seller to receive $141,000 after paying a 6% real estate commission.

So, the correct answer is $150,000.

13. Sales agent has a 60/40 split with the broker. He just sold a home for $220,000 which paid a 3% commission. How much money did the sales agent make?

$3,960

$3,300

$6,600

$2,640

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.

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.

14. Lynn Applegate buys a property for $120,000. Three years later, she sells the property for $145,000 and pays a broker's commission of 7% of the selling price. What is her rate of profit?

12.375%

11.5%

13.75%

15%

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

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%.

15. A client tells that they are willing to pay a 5% commission as long as they net $250,000 on the sale of their home. To comply with their request what would be the minimum listing price?

$259,000

$260,100

$263,158

$262,500

Explanation

16. The county-appraised market value of a property is $204,000. The county rate of assessment is 5%. The tax rate is thirty-four and one-quarter mills for the county institution tax and twenty-nine and one-half mills for the borough tax. What is the total annual tax on the property?

$10,200

$625.50

$650.25

$13,005

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 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.

17. What is 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?

$22.33

$416.48

$416.67

$5,000

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 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.

18. If a property is assessed at $5,200 and the tax rate is 84 mills, the monthly tax is:

$364.40

$436.80

$36.40

$43.80

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 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.

19. A $100,000 mortgage with a monthly payment of $950 toward the payment of principal and interest has an eight and one-half percent annual interest rate. How much of the first month's payment is applied toward the principal?

$8.50

$241.67

$267.41

708.33

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

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.

20. The sale of a home for $165,000 represents a 12% decline in price from the original listing price. If the listing agreement stipulated a 6% commission on the listing broker's sale price, what would the listing broker have earned if the home had sold for the original listing price?

$9,900

$10,284

$11,088

$11,250

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

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.