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Real Estate Math

Calculations for commission, prorations, area, and financing

200 questions10 concepts
Real Estate Math β€” Study Card
Real Estate Math study card infographic showing key concepts, exam weight (12%), and memory aids
AI-generated study card for Real Estate Math. Covers 12% of the real estate exam.
Difficulty Breakdown
Easy95 (48%)
Medium80 (40%)
Hard25 (13%)
Study Tips for Math
  • β€’Master the T-bar method for proportion problems (total on top, parts on bottom)
  • β€’Commission = Sale Price Γ— Rate; Cap Rate = NOI Γ· Value; GRM = Price Γ· Gross Rent
  • β€’Prorations: Seller pays through closing day; interest paid in arrears, taxes in advance
  • β€’Always check if the question asks for monthly or annual figures before calculating

Key Concepts

Percentage to Decimal Conversion

Converting a percentage to a decimal involves dividing the percentage value by 100.

IRV Formula

IRV stands for Income, Rate, and Value. It represents the relationship between Net Operating Income (I), Capitalization Rate (R), and Property Value (V).

Net Operating Income (NOI)

Net Operating Income (NOI) is the revenue a property generates after deducting all operating expenses.

Gross Rent Multiplier (GRM)

The gross rent multiplier (GRM) is a quick method for estimating the value of income-producing property by multiplying the property's gross rent by a factor derived from comparable sales. GRM = Sale Price / Gross Rent.

Capitalization Rate

The capitalization rate (cap rate) is the ratio of a property's net operating income to its sale price, expressed as a percentage. It is used to estimate value and compare profitability of investment properties. Cap Rate = NOI / Value.

Net Operating Income (NOI)

Net operating income (NOI) is the annual income generated by an income-producing property after deducting operating expenses, but before deducting mortgage payments, income taxes, and depreciation.

Loan Qualification Math

Loan qualification math involves calculating the debt-to-income ratios that lenders use to determine whether a borrower qualifies for a mortgage. The two primary ratios are the front-end (housing expense) ratio and the back-end (total debt) ratio.

Proration Calculations

Proration calculations divide shared expenses such as property taxes, insurance, HOA dues, and rent between buyer and seller at closing based on the number of days each party owns the property.

Commission Splits

Commission splits refer to the division of the total real estate commission among the listing and selling brokerages, and then between each broker and their respective agents. Commission rates and splits are always negotiable.

Area Calculation (Square Footage)

Area calculation involves determining the square footage or acreage of a property using geometric formulas. Key conversions: 1 acre = 43,560 square feet, 1 mile = 5,280 feet, 1 section = 640 acres.

Practice Questions

Area(17)

A lot purchased 25 years ago for $40,000 has appreciated 45% total. What is it worth today?

EASY

A lot measures 150 feet by 200 feet. How many acres is this?

MEDIUM

A lot costs $300,000. It is 100 feet wide and 150 feet deep. How much is the price per square foot?

EASY

A lot in a subdivision sells for $5.00 per square foot. It is 100 feet wide and 120 feet deep. How much does the lot cost?

EASY

A lot in a subdivision is being sold for $8.00 per square foot. It is 200 feet wide and 400 feet deep. How much does the lot cost?

EASY

A lot purchased 25 years ago for $40,000 has appreciated 45% total. What is it worth today?

EASY

What is the price per front foot for a 100' wide x 125' long lot that sold for $125,000?

EASY

A lakefront property sold for $550,000 with 550 feet of lake frontage. About how much did it sell per front foot?

EASY

A lot costs $300,000. It is 100 feet wide and 150 feet deep. How much is the price per square foot?

EASY

A lakefront property sold for $550,000 with 550 feet of lake frontage. About how much did it sell per front foot?

EASY

A lot in a subdivision sells for $5.00 per square foot. It is 100 feet wide and 120 feet deep. How much does the lot cost?

EASY

A lot in a subdivision is being sold for $8.00 per square foot. It is 200 feet wide and 400 feet deep. How much does the lot cost?

EASY

Jane learns that a lakefront property sold for $700,000 with 400 feet of lake frontage. About how much per front foot?

EASY

What is the price per front foot for a 50' wide x 100' long lot that sold for $75,000?

EASY

What is the price per front foot for a 100' wide x 125' long lot that sold for $125,000?

EASY

What is the price per front foot for a 50' wide x 100' long lot that sold for $75,000?

EASY

Jane learns that a lakefront property sold for $700,000 with 400 feet of lake frontage. About how much per front foot?

EASY

Area_and_volume(20)

A house sells for $360,000 and contains 2,550 square feet. What is the price per square foot?

MEDIUM

A warehouse is 80 feet long, 50 feet wide, and 20 feet high. What is the volume of the warehouse in cubic feet?

HARD

How many square feet are in a lot containing 1.75 acres?

MEDIUM

How many square feet are in a lot containing 1.50 acres?

HARD

A house sells for $450,000 and contains 2,550 square feet. What is the price per square foot?

MEDIUM

How many square feet are in a lot containing 2.00 acres?

MEDIUM

A house sells for $405,000 and contains 2,550 square feet. What is the price per square foot?

MEDIUM

A rectangular lot measures 135 feet by 110 feet. What is the lot area in square feet?

MEDIUM

A rectangular lot measures 105 feet by 110 feet. What is the lot area in square feet?

HARD

A house sells for $540,000 and contains 2,550 square feet. What is the price per square foot?

HARD

A house sells for $495,000 and contains 2,550 square feet. What is the price per square foot?

EASY

A rectangular lot measures 120 feet by 110 feet. What is the lot area in square feet?

MEDIUM

A triangular lot has a base of 200 feet and a height of 150 feet. What is the area of the lot?

MEDIUM

A property has an L-shaped floor plan. The main section is 40 feet by 30 feet, and the wing is 20 feet by 15 feet. What is the total living area?

HARD

A rectangular lot measures 150 feet by 110 feet. What is the lot area in square feet?

EASY

How many square feet are in a lot containing 1.00 acre?

EASY

A lot contains 65,340 square feet. How many acres is this?

EASY

A trapezoid-shaped lot has a frontage of 100 feet, a rear width of 140 feet, and a depth of 160 feet. Using the average-width method, what is the lot area?

EASY

How many square feet are in a lot containing 1.25 acres?

EASY

A rectangular lot measures 90 feet by 110 feet. What is the lot area in square feet?

EASY

Commission(33)

A property sells for $300,000. You handled the sale and get 40% of what your broker receives. The broker received $18,000. How much do you earn?

EASY

An agent received 35% share of 3% gross commission. The salesperson received $4,500. What did the property sell for?

HARD

A home you listed sells for $400,000. Your broker receives 6% and you receive 45% of their check. How much do you receive?

MEDIUM

An agent receives 50% share of a 3% gross commission. The property sold for $350,000. How much commission will the agent receive?

EASY

An agent lists a seller's house for 5% commission. The final sales price is $255,000. How much commission did the seller pay?

EASY

A broker earns 5% commission on a $600,000 sale. If the listing broker gets 60%, how much do they receive?

EASY

A 6% commission on a $250,000 sale equals:

EASY

An agent received 35% share of 3% gross commission. The salesperson received $4,500. What did the property sell for?

HARD

The broker represents both buyer and seller with 5.25% commission rate and received $8,000. What was the final sales price?

MEDIUM

With a 5.5% commission and $11,000 received by the broker, the final sale price was:

MEDIUM

A home you listed sells for $400,000. Your broker receives 6% and you receive 45% of their check. How much do you receive?

MEDIUM

A 6% commission is established. The house sells for $2,800,000. What is the commission?

EASY

A house sells for $330,000 in Albany New York. The commission check is handed to the broker which is $17,325. What was the percentage the broker received?

EASY

Timothy agrees to list his property to receive at least $100,000 after paying 5% broker's commission and $2,500 closing costs. At what price must it sell?

HARD

Timothy agrees to list his property to receive at least $100,000 after paying 5% broker's commission and $2,500 closing costs. At what price must it sell?

HARD

An agent lists a house for 6% commission. Final sales price is $555,000. How much commission did the seller pay?

EASY

A property sells for $300,000. The commission rate is 6%, split equally between listing and selling brokers. What does each broker receive?

EASY

A property in Arizona sells for $400,000. If the agent earns 3% on the first $100,000 and 2.5% on the remainder, what is the total commission?

MEDIUM

A house sells for $280,000. The commission check to the broker is $16,800. What percentage did the broker receive?

EASY

A house sells for $330,000 in Albany New York. The commission check is handed to the broker which is $17,325. What was the percentage the broker received?

EASY

+ 13 more questions

Commission_calculations(32)

A property sells for $388,000. If the broker's commission rate is 6%, what is the total commission?

EASY

A property sells for $275,000 at a commission rate of 6.0%. What is the total commission?

MEDIUM

A property sells for $300,000. The selling broker's commission rate is 2.5% of the sale price. The selling agent receives 70% of the selling broker's commission. What does the selling agent earn?

MEDIUM

$295,000 sale, 6%:

EASY

A seller closes on a property for $500,000. The commission is 6%, other seller closing costs are $4,500, and the existing mortgage payoff is $150,000. What are the seller's net proceeds before any tax effects?

MEDIUM

A seller closes on a property for $550,000. The commission is 5%, other seller closing costs are $8,200, and the existing mortgage payoff is $230,000. What are the seller's net proceeds before any tax effects?

MEDIUM

A property sells for $270,000. The listing broker receives 3% and the selling broker receives 2.5%. If the selling agent splits commissions 70/30 with their broker, what does the selling agent earn?

MEDIUM

A property sells for $380,000 at a commission rate of 5.5%. What is the total commission?

EASY

A property sells for $250,000 with a 5% commission. Total commission is:

EASY

A property sells for $350,000. The listing broker receives 3% and the selling broker receives 2.5%. If the selling agent splits their commission 65/35 with their broker, what does the selling agent earn?

MEDIUM

A seller wants to net $400,000 after paying a 5% commission and $6,000 in other closing costs. What minimum sale price is needed?

HARD

A property sells for $415,000 at a commission rate of 5.0%. What is the total commission?

MEDIUM

A seller wants to net $350,000 after paying a 6% commission and has no other closing costs to consider. What sale price is needed?

HARD

A property sells for $380,000 with a 6% commission split equally between the listing broker and the selling broker. The listing agent receives 55% of the listing broker's share. How much does the listing agent earn?

MEDIUM

A seller closes on a property for $320,000. The commission is 6%, other seller closing costs are $5,000, and the existing mortgage payoff is $170,000. What are the seller's net proceeds before any tax effects?

MEDIUM

A property sells for $310,000 at a commission rate of 5.5%. What is the total commission?

HARD

An agent received $7,200 as her share of a commission. She has a 60/40 split with her broker (agent gets 60%). What was the total commission paid to the brokerage?

EASY

A property sells for $300,000 with a 6% commission split equally between the listing broker and the selling broker. The listing agent receives 60% of the listing broker's share. How much does the listing agent earn?

EASY

A broker charges a graduated commission: 6% on the first $200,000 of the sale price and 4% on the amount above $200,000. If a property sells for $350,000, what is the total commission?

HARD

A broker earns a total commission of $18,000 on a sale. If the commission rate was 6%, what was the sale price of the property?

EASY

+ 12 more questions

Commission Calculations(21)

A property sells for $340,000. The listing broker receives 3% and the selling broker receives 2.5%. If the selling agent splits their commission 70/30 with their broker, how much does the selling agent earn?

MEDIUM

$310,000 sale, 3%/2.5%. Selling agent 70/30:

MEDIUM

A property sells for $210,000. If the total commission rate is 6%, what is the total commission earned?

EASY

A West Virginia property sells for $325,000 with a 6% commission. What is the total commission?

EASY

$285,000 sale, 6%:

EASY

A property sells for $265,000 with a 6% commission rate. What is the total commission earned?

EASY

A property sells for $258,000. If the broker's commission rate is 6%, what is the total commission earned?

EASY

$380,000 sale, 3% listing / 2.5% selling. Selling agent 70/30:

MEDIUM

A South Dakota property sells for $280,000 and the agent earns a 6% commission. What is the commission amount?

EASY

A property sold for $350,000. The listing broker receives 3% and the selling broker receives 3%. The selling agent's split with their broker is 70/30. How much does the selling agent earn?

MEDIUM

A home sells for $350,000. The listing side earns 3% and the selling side earns 2.5% of the sale price. The selling agent splits their side 70/30 with their broker. How much does the selling agent earn?

MEDIUM

A property sells for $240,000. The total commission is 5.5%, split so the listing broker receives 3% and the selling broker receives 2.5%. The selling agent receives 65% of their broker's share. What does the selling agent earn?

MEDIUM

$300,000 sale, 6% commission:

EASY

A property sells for $310,000. If the total commission rate is 6%, what is the total commission earned?

EASY

A property sells for $375,000 with a total commission rate of 6%. What is the total commission earned?

EASY

$320,000 sale, 6% commission:

EASY

A property sells for $280,000. The listing broker charges a 3% commission and the buyer's broker charges 2.5%. The selling agent receives 65% of the buyer's broker commission. What does the selling agent earn?

MEDIUM

A property sells for $280,000. The listing broker earns a 3% commission and the selling broker earns a separate 2.5% commission. The selling agent receives 65% of the selling broker's commission. What does the selling agent earn?

MEDIUM

$400,000 sale, 3% listing / 2.5% selling. Selling agent 70/30 split:

MEDIUM

$420,000 sale, 3%/2.5%. Selling agent 65/35:

MEDIUM

+ 1 more questions

Real Estate Math: What You Need to Know

Real Estate Math is one of the highest-weighted exam topics and the one that causes the most anxiety for test-takers. The good news is that most real estate math uses basic arithmetic with a handful of standard formulas β€” no advanced mathematics required.

The most important formulas to memorize are: Commission = Sale Price Γ— Rate, Cap Rate = NOI Γ· Value (or Value = NOI Γ· Cap Rate), GRM = Price Γ· Annual Gross Rent, LTV = Loan Amount Γ· Appraised Value, and Property Tax = Assessed Value Γ— Tax Rate. The T-bar method (also called the "magic T") is your best friend for solving proportion problems β€” put the total on top and the two parts that multiply to equal it on the bottom.

Prorations at closing are frequently tested and require careful attention to dates and the direction of charges. Remember that the seller is responsible for costs through the day of closing and the buyer from the day after. Interest on mortgage loans is paid in arrears (for the previous month), while property taxes and HOA dues are typically paid in advance. Practice converting between annual, monthly, and daily amounts, and always double-check whether a question asks for monthly or annual figures.

Frequently Asked Questions

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