A commission of $12,750 was paid at 5% of the sale price. What was the sale price?Answer: $255,000. Source: Own question; the answer is in the question itself and is worked out again
A firm receives $9,000 of commission on a sale. Its agreement with the agent gives the agent 70% of what the firm receives. What is the agent's share?Answer: $6,300. Source: Own question; the answer is in the question itself and is worked out again
A house sells for $325,000 and the listing agreement sets the commission at 6% of the sale price. What is the total commission?Answer: $19,500. Source: Own question; the answer is in the question itself and is worked out again
A leasing fee is 4% of the total rent over a 3-year lease at $2,500 a month. What is the fee?Answer: $3,600. Source: Own question; the answer is in the question itself and is worked out again
Show all 72 questions (68 more)
Commissions and fees, continued
A listing pays 7% on the first $100,000 of the sale price and 4% on the rest. The property sells for $260,000. What is the total commission?Answer: $13,400. Source: Own question; the answer is in the question itself and is worked out again
A property manager charges 8% of the rent collected. In one month the manager collects $1,450 from each of 6 units. What is the management fee for the month?Answer: $696. Source: Own question; the answer is in the question itself and is worked out again
A property manager is paid a flat $75 per unit each month plus 5% of the rent collected. The building has 12 units and $15,600 of rent is collected in the month. What is the manager's pay for the month?Answer: $1,680. Source: Own question; the answer is in the question itself and is worked out again
A sale closes at $198,400 with a 5.5% commission. What is the commission?Answer: $10,912. Source: Own question; the answer is in the question itself and is worked out again
A seller paid $16,800 in commission on a $280,000 sale. What commission rate was charged?Answer: 6%. Source: Own question; the answer is in the question itself and is worked out again
An agent wants to earn $4,200 from a sale. The firm receives 3% of the sale price and pays the agent 50% of that. What sale price gives the agent $4,200?Answer: $280,000. Source: Own question; the answer is in the question itself and is worked out again
The total commission on a sale is $14,400. The listing firm keeps 55% and pays the rest to the selling firm. How much does the selling firm receive?Answer: $6,480. Source: Own question; the answer is in the question itself and is worked out again
Two firms split a 6% commission equally on a $410,000 sale. The selling agent then receives 60% of her firm's half. How much does the selling agent receive?Answer: $7,380. Source: Own question; the answer is in the question itself and is worked out again
Profit, loss and return 12
A house valued at $200,000 gains 4% in value each year, with each year's gain figured on the new value. What is its value after 2 years?Answer: $216,320. Source: Own question; the answer is in the question itself and is worked out again
A lot bought for $80,000 is sold for $92,000. What is the profit as a percent of the purchase price?Answer: 15%. Source: Own question; the answer is in the question itself and is worked out again
A property bought for $150,000 rose in value by 20% and then fell by 10% of the new value. What is it worth now?Answer: $162,000. Source: Own question; the answer is in the question itself and is worked out again
A property sold for $345,000, which gave the seller a 15% profit on the original cost. What was the original cost?Answer: $300,000. Source: Own question; the answer is in the question itself and is worked out again
A rental building takes in $96,000 of gross income a year and has $38,400 of operating expenses. What is the net operating income?Answer: $57,600. Source: Own question; the answer is in the question itself and is worked out again
A rental house brings in $1,900 a month. Yearly expenses are $7,300. The owner paid $310,000 in cash. What is the yearly return on the purchase price?Answer: 5%. Source: Own question; the answer is in the question itself and is worked out again
An investor pays $500,000 in cash for a building that produces $42,500 of net operating income a year. What is the yearly return on the investment?Answer: 8.5%. Source: Own question; the answer is in the question itself and is worked out again
An investor puts $60,000 of her own cash into a property. After all expenses and loan payments the property leaves $5,400 a year. What is the cash-on-cash return?Answer: 9%. Source: Own question; the answer is in the question itself and is worked out again
An owner bought a house for $310,000, spent $25,000 on improvements and sold it for $368,500. What is the profit as a percent of the total cost (purchase plus improvements)?Answer: 10%. Source: Own question; the answer is in the question itself and is worked out again
An owner paid $240,000 for a house and later accepts $216,000 for it. Find the percent lost on what the owner paid.Answer: 10%. Source: Own question; the answer is in the question itself and is worked out again
An owner writes off a building that cost $275,000 in equal parts over 27.5 years. How much is written off in one year?Answer: $10,000. Source: Own question; the answer is in the question itself and is worked out again
Land bought for $45,000 is sold 5 years later for $58,500. What is the average gain per year as a percent of the purchase price, not compounded?Answer: 6%. Source: Own question; the answer is in the question itself and is worked out again
Area and price per unit 12
A builder pays $2.75 a square foot for a lot 110 feet by 150 feet. What does the lot cost?Answer: $45,375. Source: Own question; the answer is in the question itself and is worked out again
A house is L-shaped: a 40 by 30 foot rectangle joined to a 20 by 15 foot rectangle. What is the total floor area?Answer: 1,500 square feet. Source: Own question; the answer is in the question itself and is worked out again
A house with 1,850 square feet of floor area is listed at $333,000. What is the list price per square foot?Answer: $180. Source: Own question; the answer is in the question itself and is worked out again
A lot is a right triangle whose two short sides measure 90 feet and 120 feet. What is its area?Answer: 5,400 square feet. Source: Own question; the answer is in the question itself and is worked out again
A lot is a trapezoid. Its two parallel sides are 100 feet and 140 feet, and they are 90 feet apart. What is its area?Answer: 10,800 square feet. Source: Own question; the answer is in the question itself and is worked out again
A lot with 75 feet of street frontage sells for $90,000. What is the price per front foot?Answer: $1,200. Source: Own question; the answer is in the question itself and is worked out again
A rectangular lot has an area of 9,600 square feet and is 80 feet wide. How deep is it?Answer: 120 feet. Source: Own question; the answer is in the question itself and is worked out again
A rectangular lot is 80 feet wide and 125 feet deep. What is its area?Answer: 10,000 square feet. Source: Own question; the answer is in the question itself and is worked out again
A room is 18 feet by 24 feet. How many square yards of carpet cover the floor? (One square yard is 9 square feet.)Answer: 48 square yards. Source: Own question; the answer is in the question itself and is worked out again
Convert a parcel of 65,340 square feet to acres, at 43,560 square feet to the acre.Answer: 1.5 acres. Source: Own question; the answer is in the question itself and is worked out again
How many square feet are in 2.5 acres? (One acre is 43,560 square feet.)Answer: 108,900 square feet. Source: Own question; the answer is in the question itself and is worked out again
Land sells for $12,000 an acre. What does a rectangular parcel 660 feet by 1,320 feet cost? (One acre is 43,560 square feet.)Answer: $240,000. Source: Own question; the answer is in the question itself and is worked out again
Loans and interest 12
A 30-year loan of $200,000 has a monthly principal and interest payment of $1,199. If every payment is made, how much interest is paid over the life of the loan?Answer: $231,640. Source: Own question; the answer is in the question itself and is worked out again
A borrower pays a 1% origination fee and 1.5 discount points on a $160,000 loan, where one point is 1% of the loan. What is the total charge?Answer: $4,000. Source: Own question; the answer is in the question itself and is worked out again
A buyer puts $36,000 down, which is 15% of the price. What is the price?Answer: $240,000. Source: Own question; the answer is in the question itself and is worked out again
A home is worth $325,000 and the loan balance is $208,000. What is the owner's equity as a percent of the value?Answer: 36%. Source: Own question; the answer is in the question itself and is worked out again
A lender allows a housing payment of up to 28% of gross monthly income. A borrower earns $6,500 a month before tax. What is the largest housing payment allowed?Answer: $1,820. Source: Own question; the answer is in the question itself and is worked out again
A lender allows total monthly debt payments of up to 36% of gross monthly income. A borrower earns $7,000 a month and already pays $520 a month on other debts. What is the largest housing payment allowed?Answer: $2,000. Source: Own question; the answer is in the question itself and is worked out again
A lender charges 2 discount points on a $215,000 loan. One point is 1% of the loan amount. What do the points cost?Answer: $4,300. Source: Own question; the answer is in the question itself and is worked out again
A lender will lend 80% of a home's appraised value. The home appraises at $290,000. What is the largest loan?Answer: $232,000. Source: Own question; the answer is in the question itself and is worked out again
A loan balance is $150,000 at 6% a year. The monthly principal and interest payment is $900. What is the balance after one payment?Answer: $149,850. Source: Own question; the answer is in the question itself and is worked out again
A loan has a balance of $180,000 at 5% a year, and the monthly principal and interest payment is $966. How much of the next payment goes to principal?Answer: $216. Source: Own question; the answer is in the question itself and is worked out again
A loan of $240,000 carries simple interest at 6% a year. How much interest is due for one month?Answer: $1,200. Source: Own question; the answer is in the question itself and is worked out again
The payment factor for a loan is $6.32 a month for each $1,000 borrowed. What is the monthly principal and interest payment on a $185,000 loan?Answer: $1,169.20. Source: Own question; the answer is in the question itself and is worked out again
Proration and closing 12
A buyer pays $250,000 for a home, with a $200,000 loan and $6,200 of closing costs. The buyer already gave $5,000 in earnest money. How much cash must the buyer bring to closing?Answer: $51,200. Source: Own question; the answer is in the question itself and is worked out again
A home sells for $300,000. The seller pays a 6% commission, $2,400 of other closing costs and a $175,000 loan payoff. What does the seller net?Answer: $104,600. Source: Own question; the answer is in the question itself and is worked out again
A monthly rent of $1,240 is prorated for a 31-day month. The tenant moves in on day 22 and pays for day 22 through day 31. How much is due?Answer: $400. Source: Own question; the answer is in the question itself and is worked out again
A new loan of $216,000 at 5% a year closes with 10 days left in the month. Using a 360-day year, how much interest is collected at closing for those 10 days?Answer: $300. Source: Own question; the answer is in the question itself and is worked out again
A seller must pay off a $140,900 loan and $3,500 in closing costs, and wants $41,600 left after a 7% commission. What sale price is needed?Answer: $200,000. Source: Own question; the answer is in the question itself and is worked out again
A seller wants to net $188,000 after paying a 6% commission, with no other costs. What is the lowest sale price that does it?Answer: $200,000. Source: Own question; the answer is in the question itself and is worked out again
A seller's closing statement shows a $260,000 sale price as a credit, and debits of $15,600 commission, $151,300 loan payoff and $1,900 of prorated tax. What is the cash due to the seller?Answer: $91,200. Source: Own question; the answer is in the question itself and is worked out again
Annual property tax of $3,650 is unpaid and is prorated by a 365-day year. The seller owes for 146 days. What is the seller's share?Answer: $1,460. Source: Own question; the answer is in the question itself and is worked out again
At closing a lender collects 3 months of property tax and 2 months of insurance for an escrow account. The tax is $2,400 a year and the insurance is $900 a year. How much is collected?Answer: $750. Source: Own question; the answer is in the question itself and is worked out again
Homeowners' association dues of $1,095 for the calendar year were paid in advance by the seller. Using a 365-day year, the buyer will own the home for 200 days of the year. How much does the buyer pay back to the seller?Answer: $600. Source: Own question; the answer is in the question itself and is worked out again
Property tax of $2,920 for the calendar year was paid by the seller in January. The buyer owns the home for the last 100 days of a 365-day year. How much does the buyer owe the seller for tax?Answer: $800. Source: Own question; the answer is in the question itself and is worked out again
Rent of $1,500 for a 30-day month was collected by the seller on the first. The buyer owns the property for the last 12 days of the month. How much rent is credited to the buyer?Answer: $600. Source: Own question; the answer is in the question itself and is worked out again
Property tax and value 12
A building could collect $120,000 a year if full. Vacancy and collection loss is 5% and operating expenses are $41,000. What is the net operating income?Answer: $73,000. Source: Own question; the answer is in the question itself and is worked out again
A building has an effective age of 10 years and a total economic life of 50 years. By the age-life method, what percent of its cost new has been lost to depreciation?Answer: 20%. Source: Own question; the answer is in the question itself and is worked out again
A building produces $54,000 of net operating income a year. With a capitalization rate of 9%, what value does direct capitalization give?Answer: $600,000. Source: Own question; the answer is in the question itself and is worked out again
A comparable house sold for $285,000. It has a garage worth $12,000 that the subject house lacks, and it lacks a deck worth $5,000 that the subject has. What is the adjusted price of the comparable?Answer: $278,000. Source: Own question; the answer is in the question itself and is worked out again
A county assesses property at 40% of market value. A home has a market value of $350,000 and the tax rate is $2 per $100 of assessed value. What is the yearly tax?Answer: $2,800. Source: Own question; the answer is in the question itself and is worked out again
A home is assessed at $180,000 and the tax rate is $1.25 per $100 of assessed value. What is the yearly tax?Answer: $2,250. Source: Own question; the answer is in the question itself and is worked out again
A home pays county tax of $0.60 per $100 and city tax of $0.45 per $100 on an assessed value of $220,000. What is the total yearly tax?Answer: $2,310. Source: Own question; the answer is in the question itself and is worked out again
A property is assessed at $240,000 and the tax rate is 18 mills. A mill is $1 of tax per $1,000 of value. What is the yearly tax?Answer: $4,320. Source: Own question; the answer is in the question itself and is worked out again
A store lease sets rent at $2,000 a month plus 3% of gross sales over $500,000 a year. The store's sales for the year are $650,000. What is the total rent for the year?Answer: $28,500. Source: Own question; the answer is in the question itself and is worked out again
An apartment building has 40 units and 3 are vacant. What is the vacancy rate?Answer: 7.5%. Source: Own question; the answer is in the question itself and is worked out again
An investor pays $800,000 for a property that nets $60,000 a year after operating expenses. What capitalization rate does that price imply?Answer: 7.5%. Source: Own question; the answer is in the question itself and is worked out again
By the cost approach, a house of 2,000 square feet would cost $150 a square foot to build new. It has lost 20% of that to depreciation, and the land is worth $70,000. What is the estimate of value?Answer: $310,000. Source: Own question; the answer is in the question itself and is worked out again
How this list was compiled: Our own arithmetic questions. Every price, rate, fee, tax bill, lot size and date is made up for the drill and none is a real statistic, a market figure or a rate set by any law. The answer to each is arithmetic on the numbers in the question, worked out when the bank was written and again from the numbers read back out of the question text (2026-10-04). The kinds of calculation follow the math lines of two outlines published by state real estate commissions, both read 2026-10-04: the North Carolina Real Estate Commission's examination content outline in Real Estate Licensing in North Carolina, April 2026 (https://www.ncrec.gov/Pdfs/Licensing/RELINC.pdf), with Section XVI of its Prelicensing Course Syllabus, March 2024 edition amended May 2026 (https://www.ncrec.gov/Forms/Education/Prelicense_Course_Syllabus.pdf), and the Texas Real Estate Commission's Principles of Real Estate II course outline, form PRINS 2-0 (https://www.trec.texas.gov/sites/default/files/pdf-forms/PRINS2-0.pdf). One value is given inside the questions that use it: 43,560 square feet to the acre. Licence: Questions, choices and explanations are original work of this site.
How it works
These real estate math practice problems are arithmetic of our own: commissions, profit, lot area, loan interest, prorations and property tax. Every number needed is in the question, and every answer is worked out step by step.
Read the full guide
What is left out
No state's law, tax rate or fee schedule is used, and no licensing exam or testing company's sample test is copied, so no exam length or pass mark is implied.
Six topics
The Start from menu under the question holds the topics: commissions and fees, profit, loss and return, area and price per unit, loans and interest, proration and closing, or property tax and value. Every price, rate and date is made up.
Paper test
After a set, Print makes a paper copy of it. Exam mode draws 20, our number, with no time limit.
To go from a commission back to a price, divide by the rate; from a net amount, divide by 100% minus the rate.
A proration is an amount per day times a number of days, and each question states its own day count.
After a set, More options lets you ask only the questions you Missed. Clear my progress, in the same place, erases what this browser keeps.
Questions and answers
What kinds of real estate math questions are here?
Six: commissions and fees, profit and return, area and price per unit, loan interest and payments, prorations and closing figures, and property tax and value. The kinds follow math lines in outlines published by the North Carolina and Texas real estate commissions.
How do you work out a commission?
Multiply the sale price by the rate: $325,000 at 6% is 325,000 x 0.06 = $19,500. To go from a commission back to a price, divide by the rate instead.
How is a proration figured?
Divide the amount by the days in its period, then multiply by the days owed. A $3,650 tax bill over a 365-day year is $10 a day, so 146 days come to $1,460.
How many square feet are in an acre?
43,560. So 2.5 acres is 2.5 x 43,560 = 108,900 square feet, and a parcel of 65,340 square feet is 65,340 / 43,560 = 1.5 acres. The questions that need the figure give it.
Is this a real estate math practice exam from a real licensing test?
No. These real estate math practice questions are unofficial and written for this site. No question comes from a real exam, a testing company's sample test or a prep book, and no exam length or pass mark is implied.