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Real Estate Math

Calculations for commission, prorations, area, and financing

138 questions10 concepts
Real Estate Math — 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
Easy73 (53%)
Medium52 (38%)
Hard13 (9%)
Study Tips for Math
  • Master the T-bar method for proportion problems (total on top, parts on bottom)
  • Commission = Sale Price × Rate; Cap Rate = NOI ÷ Value; GRM = Price ÷ Gross Rent
  • Prorations: Seller pays through closing day; interest paid in arrears, taxes in advance
  • 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(18)

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

EASY

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

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

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

A man died without a will and with no sur- viving relatives. His four-acre farm will

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 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 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 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 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

Commission(37)

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 sells for $325,000. If the commission is 6%, split equally between listing and selling brokers, what does each broker receive?

EASY

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

EASY

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

EASY

A Texas agent earns a 6% commission on a $350,000 sale. The listing broker takes 60% of the commission. How much does the listing broker 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 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 $280,000. The commission check to the broker is $16,800. What percentage did the broker receive?

EASY

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

MEDIUM

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

The Real Estate Commissioner’s rules:

EASY

During a listing agreement, a 6% commission is established. The house sells for $450,000. What is the commission?

EASY

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

MEDIUM

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

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

A house sells for $2,500,000. The commission check to the broker is $137,500. What percentage did the broker receive?

EASY

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

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

EASY

+ 17 more questions

Interest(22)

All of the following are sufficient to transfer an interest in real estate, except:

HARD

If Amanda's gross income is $8,550 monthly, she would need to spend less than ___ in total household debt to qualify for most loans (using 28/36 rule).

EASY

What is the interest rate on a $200,000 loan requiring an annual interest payment of $8,000?

EASY

The buyer gets a $280,000 mortgage in Florida. The intangible tax is:

MEDIUM

What is the annual interest rate on a $300,000 loan requiring a monthly interest payment of $500?

EASY

If Amanda's gross income is $8,550 monthly, she would need to spend less than ___ in total household debt to qualify for most loans (using 28/36 rule).

EASY

What is the interest rate on a $200,000 loan requiring an annual interest payment of $8,000?

EASY

If a bank makes an 85% loan on a house valued at $120,000, how much cash is required at closing if the buyer already paid $8,000 earnest money?

MEDIUM

What is the interest rate on a $150,000 loan requiring an annual interest payment of $6,500?

EASY

What is the annual interest rate on a $300,000 loan requiring a monthly interest payment of $500?

EASY

Using the 28/36 rule, if Marty's gross income is $5,500 monthly, he needs to spend less than ___ in housing costs to qualify for most loans.

EASY

Using the 28/36 rule, if Marty's gross income is $5,500 monthly, he needs to spend less than ___ in housing costs to qualify for most loans.

EASY

If a bank makes a 90% loan on a house valued at $88,500, how much cash is required at closing if the buyer already paid $4,000 in earnest money?

MEDIUM

Which of the following is of least interest to an appraiser?

EASY

Which of the following instruments does NOT transfer an interest in real property?

HARD

The degree, quantity, or nature of a person’s interest in real property is called his

EASY

In a deed that states “to Jonathon for his life,” the grantor has what type of interest?

EASY

If a bank makes an 85% loan on a house valued at $120,000, how much cash is required at closing if the buyer already paid $8,000 earnest money?

MEDIUM

A buyer obtains a loan for $200,000 at 6% annual interest. What is the monthly interest payment for the first month?

EASY

What is the interest rate on a $150,000 loan requiring an annual interest payment of $6,500?

EASY

+ 2 more questions

Prorations(26)

Gina buys a property where the seller prepaid quarterly taxes of $750. She closes on March 1st. How much does she owe the seller?

MEDIUM

Gina buys a property where the seller prepaid quarterly taxes of $750. She closes on March 1st. How much does she owe the seller?

MEDIUM

James buys a property closing June 1st. The seller prepaid annual taxes of $3,000. How much does James owe the seller?

MEDIUM

Newton buys a property closing September 1st. The seller prepaid annual taxes of $2,000. How much does Newton owe the seller?

MEDIUM

A property's market value is $250,000. The assessment rate is 15% with 27.50 mills. Find the annual property taxes.

MEDIUM

A property has annual property taxes of $3,600. The seller paid taxes through December 31, but the sale closes on October 1. How much does the seller owe the buyer as a proration?

HARD

A property's market value is $450,000. Assessment rate is 25% with 70.50 mills. Find the annual property taxes.

MEDIUM

Property taxes on a Texas home are $6,000 per year. The sale closes on April 1. How much does the seller owe for prorated taxes?

MEDIUM

A property's market value is $750,000. The assessment rate is 25% with 23.50 mills. Find the annual property taxes.

MEDIUM

Jon buys a property closing on March 1st. The seller prepaid annual taxes of $6,000. How much does Jon owe the seller?

MEDIUM

A property's market value is $2,250,000. The assessment rate is 15% with 28.55 mills. Find the annual property taxes.

MEDIUM

A property's market value is $250,000. The assessment rate is 15% with 27.50 mills. Find the annual property taxes.

MEDIUM

A property's market value is $450,000. Assessment rate is 25% with 70.50 mills. Find the annual property taxes.

MEDIUM

A property's market value is $350,000. The assessment rate is 25% with 27.50 mills. Find the annual property taxes.

MEDIUM

Annual property taxes are $4,380. The property closes on March 15. If the seller has NOT paid taxes for the current year, how much does the seller owe at closing? (Use 365 days)

HARD

Jon buys a property closing on March 1st. The seller prepaid annual taxes of $6,000. How much does Jon owe the seller?

MEDIUM

A property's market value is $350,000. The assessment rate is 25% with 27.50 mills. Find the annual property taxes.

MEDIUM

A property's market value is $2,250,000. The assessment rate is 15% with 28.55 mills. Find the annual property taxes.

MEDIUM

A property's market value is $400,000. Assessment rate is 25% with 22.75 mills and $30,000 property tax deduction. Find annual property taxes.

HARD

Newton buys a property closing September 1st. The seller prepaid annual taxes of $2,000. How much does Newton owe the seller?

MEDIUM

+ 6 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 — no advanced mathematics required.

The most important formulas to memorize are: Commission = Sale Price × Rate, Cap Rate = NOI ÷ Value (or Value = NOI ÷ Cap Rate), GRM = Price ÷ Annual Gross Rent, LTV = Loan Amount ÷ Appraised Value, and Property Tax = Assessed Value × Tax Rate. The T-bar method (also called the "magic T") is your best friend for solving proportion problems — 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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