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Real Estate Exam Math — Every Formula You Need (Worked Examples)

Math is where most candidates lose the real estate exam. Not because the math is hard — it isn't. It's seventh-grade arithmetic dressed up in adult clothes. People fail because they freeze, can't remember which number goes on top, and waste twelve minutes on a question that should take ninety seconds.

This guide fixes that. Every formula you need. Every calculation type that shows up on the salesperson and broker exams. Worked numbers. No fluff. By the end you'll have a cheat sheet in your head and a process you can run on autopilot.

The T-Method — Your Backbone for Almost Every Problem

If you remember nothing else, remember the T.


   Part
 -------
 Whole | Rate

Cover up what you're solving for. The other two tell you what to do. Commission, taxes, interest, profit percentages, area conversions — they all collapse into the T. Master this and you've already won half the math section.

Commission Problems

Commission is the most common math question on the exam. Expect at least three.

Problem 1 — Basic Commission

A house sells for $425,000 at a 6% total commission. The listing broker and selling broker split 50/50. The listing agent gets 60% of their broker's share. What does the agent earn?

Problem 2 — Back-Solving the Rate

You sold a property for $312,000 and your office collected $18,720 in commission. What was the commission rate?

Problem 3 — Back-Solving the Sale Price

A broker collected $14,400 at a 4.5% commission rate. What did the property sell for?

One legal note before you move on: under Section 1 of the Sherman Antitrust Act of 1890, brokers cannot agree with competing brokers to fix commission rates. Commission is always negotiable between broker and client. The exam loves testing this — math problems sometimes hide a Sherman Act trap in the wording.

Area and Square Footage

Area shows up in lot questions, building questions, and price-per-square-foot questions.

Core formulas

Problem 4 — Lot Size

A rectangular lot measures 75 feet wide by 120 feet deep. How many square feet? What fraction of an acre?

Problem 5 — Triangular Parcel

A triangular lot has a base of 80 feet and a height of 60 feet. Find the area.

Problem 6 — Price Per Square Foot

A 2,100 sq ft house sold for $367,500. What was the price per square foot?

Proration at Closing

Proration is the math of splitting bills at closing — taxes, insurance, HOA dues, rent. RESPA (the Real Estate Settlement Procedures Act, 12 U.S.C. §§ 2601–2617) requires these amounts to show up on the closing disclosure so the buyer can see exactly what they're paying. The settlement agent calculates them, but you need to know how on the exam.

Two methods exist:

Your state will test one or both. Read the question carefully.

Problem 7 — 365-Day Proration (Taxes Paid in Arrears)

Annual property tax is $4,380. Closing date is June 15. Seller pays through the day before closing. Use the 365-day method. What does the seller owe?

Problem 8 — 360-Day Proration

Same numbers, banker's year.

Watch the wording. "Through the day of closing" means the seller pays one more day. "Up to the day of closing" means they stop the day before. Read it twice.

Loan-to-Value (LTV)

LTV is the loan amount divided by the property value (or sale price, whichever is lower).

LTV = Loan ÷ Value

Problem 9 — Standard LTV

Home costs $350,000. Down payment is $52,500. What's the LTV?

Anything over 80% typically triggers private mortgage insurance (PMI) on conventional loans. The Truth in Lending Act (TILA, Pub. L. 90-321) and Regulation Z (12 CFR 1026) require lenders to disclose the APR, finance charge, and total payments in standardized form so the borrower can compare loans on an apples-to-apples basis. Expect a TILA disclosure question paired with LTV math.

Discount Points and Origination Fees

One point = 1% of the loan amount (not the purchase price — exam trap).

Problem 10 — Cost of Points

Loan amount $320,000. Borrower pays 2 discount points plus a 1% origination fee. What's the total upfront cost?

Discount points are prepaid interest that buy down the rate. Origination fees are the lender's processing charge. Both must appear on the Loan Estimate and Closing Disclosure under Regulation Z and RESPA.

Capitalization Rate (Cap Rate)

Cap rate is how investors compare income properties. Memorize the IRV triangle:


     I (NOI)
   ---------
   R | V

NOI = Net Operating Income = gross income − operating expenses. It does not include debt service or income tax.

Problem 11 — Solving for Cap Rate

A duplex generates $48,000 NOI annually and sold for $600,000. What's the cap rate?

Problem 12 — Solving for Value

An investor wants a 7.5% cap rate. A property produces $60,000 NOI. What's the maximum the investor should pay?

Higher cap rate = lower price = higher risk. Lower cap rate = higher price = perceived stability. That intuition saves you on at least one exam question.

Gross Rent Multiplier (GRM)

GRM is a quick-and-dirty valuation tool. It uses gross rent, not net.

GRM = Sale Price ÷ Gross Rent

Watch whether the problem uses monthly or annual rent — they'll trip you up.

Problem 13 — Monthly GRM

A rental house sold for $240,000. Monthly rent is $1,600. What's the monthly GRM?

Problem 14 — Estimating Value with GRM

A comparable property has a monthly GRM of 145. The subject property rents for $2,100/month. Estimated value?

Property Tax — The Mill Rate

A mill = $1 per $1,000 of assessed value. Or $0.001 per dollar. Same thing.

Annual tax = (Assessed Value ÷ 1,000) × Mill Rate

Problem 15 — Mill Calculation

Assessed value is $280,000. Tax rate is 22 mills. What's the annual tax?

Some states quote the rate as a percentage of assessed value instead — 22 mills = 2.2% — same answer, just different form.

Qualifying Ratios

Lenders use two ratios to decide if a borrower can afford a loan:

PITI = Principal, Interest, Taxes, Insurance.

Problem 16 — Maximum Housing Payment

Borrower earns $7,200/month gross. Has a $400 car payment and $250 student loan payment. Lender uses 28% front-end and 36% back-end. What's the maximum PITI they qualify for?

Quick legal pairing: the Equal Credit Opportunity Act (ECOA, 15 U.S.C. § 1691) prohibits a lender from discriminating in any aspect of a credit transaction based on race, color, religion, national origin, sex, marital status, age, or receipt of public assistance. The ratios apply to the income — not the borrower's demographics. Income from alimony, child support, Social Security, or part-time work must be counted. The exam will absolutely test this overlap.

Profit, Loss, and Percentage Change

% Change = (New − Old) ÷ Old

Problem 17 — Profit Percentage

Investor bought a flip for $185,000, put $22,000 into it, sold for $260,000. What's the profit percentage on total cost?

Problem 18 — Appreciation

A home was purchased for $310,000 four years ago. It's now worth $372,000. What's the total appreciation percentage?

Simple Interest

Interest = Principal × Rate × Time

Time is in years (or fractions of a year).

Problem 19 — Annual Interest

A $245,000 loan at 6.5% interest. How much interest in the first year?

Problem 20 — Monthly Interest

Same loan. How much of the first monthly payment goes to interest?

That's why early mortgage payments are mostly interest — the principal balance is huge.

Equity

Equity = Market Value − Mortgage Balance

Problem 21 — Calculating Equity

Home worth $475,000. Current mortgage balance $312,000. Equity?

Down Payment Problems

Problem 22 — Working Backwards from Down Payment

A buyer puts $84,000 down, which is 20% of the purchase price. What's the sale price?

Closing Cost Splits and Transfer Taxes

Transfer tax (sometimes called documentary stamps or deed tax) varies by state but is usually quoted per $100 or per $500 of sale price.

Problem 23 — Transfer Tax

State charges $0.70 per $100 of sale price. Property sells for $385,000. What's the transfer tax?

The Exam Strategy That Actually Works

Here's the process. Use it on every math question.

  1. Read the whole problem before touching the calculator. Underline what they're asking for. Half of all wrong answers come from solving for the wrong unknown.
  2. Write down what you know in dollar/percentage form. Convert percentages to decimals before plugging in.
  3. Draw the T (or IRV). Cover what you need. Read what's left.
  4. Check units. Monthly vs annual. Loan amount vs sale price. Days the seller owned vs days they didn't.
  5. Sanity check the answer. If a commission of $250,000 falls out, you multiplied somewhere you should have divided.

Pick a multiple-choice answer that's mathematically possible. If three answers are within $50 of each other and one is wildly different, the outlier is almost always a distractor.

The Federal Law You Need Alongside the Math

The math doesn't live in a vacuum. Three federal statutes show up wrapped around calculation questions constantly:

Pair these with the Fair Housing Act (Title VIII of the Civil Rights Act of 1968, as amended in 1974 and 1988) and you've covered the legal infrastructure that surrounds every dollar figure on the closing table.

Your Cheat Sheet, One More Time

Tape that to your bathroom mirror for a week. By exam day it'll be muscle memory.

Keep Going

Math is a quarter of the exam. The other three-quarters is law, contracts, agency, financing, and property rights. If you want every formula, statute, and concept in one place — built around the same plain-English, no-BS style as this guide — grab the National Real Estate Master Guide at studystack.org. It's the same playbook thousands of candidates have used to pass on the first try. Stop guessing what's on the test. Start knowing.

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