Real Estate Exam Math Practice Problems Solved
Real estate exam math practice problems fall into about six formula families: commission, proration, loan-to-value, transfer tax, area, and PITI. Together they typically make up around 6 to 10 percent of a state licensing exam. Below we work ten real problems start to finish, formula, substitution, and answer, using the same categories testing vendors actually publish.
The math section scares people more than it should, mostly because most study guides show a formula and never show it actually get used. We built these ten problems around the exact calculation categories a state testing vendor’s own content outline tests, seller’s net proceeds, prorations, transfer fees, loan-to-value, PITI, and capitalization rate, and we solve every one step by step instead of just handing you the final number.
What kinds of math actually show up on the exam?
Real estate exam math questions cluster around six formula families: commission (including splits), simple interest and loan payments, loan-to-value, property tax and proration, transfer tax, and area or square footage, according to a 2026 real estate math guide from U.S. Realty Training. On Colorado’s PSI broker exam, “Real Estate Calculations” is its own scored category worth 6 percent of the national portion, covering seller’s net proceeds, buyer funds needed at closing, property tax prorations, transfer fees, PITI estimates, equity, capitalization rate, loan-to-value, and discount points, per PSI’s Real Estate Candidate Information Bulletin for Colorado, current as of 2026.
That’s a smaller share of the exam than people assume, usually in the range of 6 to 10 percent of total questions depending on the state, but it’s disproportionately responsible for failed attempts because the questions require two or three steps instead of one. Missing a single conversion, days to a proration, points to dollars, sinks the whole problem even when the underlying concept was understood.
How do commission and commission-split problems work?
Commission problems start with a straight percentage of sale price, then usually add a split between brokerages and between broker and agent. A house sells for $340,000 under a 6 percent listing agreement.
Formula: Commission = sale price x commission rate. Substitution: $340,000 x 0.06. Answer: $20,400 total commission.
Now split it. The listing brokerage and selling brokerage split that $20,400 fifty-fifty, and the buyer’s agent keeps 60 percent of their brokerage’s half under their agent agreement.
Formula: Agent’s share = (total commission / 2) x agent’s split percentage. Substitution: ($20,400 / 2) x 0.60 = $10,200 x 0.60. Answer: $6,120 to the buyer’s agent.
How does a loan-to-value problem work?
Loan-to-value (LTV) compares the loan amount to the property’s appraised value, and the exam usually gives you two of the three numbers (loan, value, LTV) and asks for the third. A home appraises at $250,000, and the buyer is approved for a $200,000 loan.
Formula: LTV = loan amount / appraised value. Substitution: $200,000 / $250,000. Answer: 0.80, or 80 percent LTV.
How do we work a property tax proration problem?
Proration splits an annual cost between buyer and seller based on how much of the year each one owned the property, and it’s the single question type most candidates get wrong first. Annual property taxes are $3,650, paid in arrears, and the sale closes on June 30 with the seller responsible through the day of closing.
Formula: Daily rate = annual tax / 365; seller’s share = daily rate x days owned. Substitution: $3,650 / 365 = $10 per day. January 1 through June 30 is 181 days. $10 x 181. Answer: $1,810 owed by the seller, credited to the buyer at closing since the seller hasn’t paid the tax yet.
How do transfer taxes get calculated?
Transfer tax, often called documentary stamp tax, is charged on the deed, and sometimes separately on a new mortgage note, at a rate set by the state per $100 or $1,000 of value. Florida charges $0.70 per $100 on the deed and $0.35 per $100 on a new mortgage note, plus a separate 0.2 percent nonrecurring intangible tax on the new loan amount, according to the Florida Department of Revenue’s documentary stamp tax page, current as of 2026. A home sells for $300,000 with a new $240,000 loan.
Formula: Deed tax = (sale price / 100) x $0.70; note tax = (loan amount / 100) x $0.35; intangible tax = loan amount x 0.002. Substitution: ($300,000 / 100) x 0.70 = $2,100. ($240,000 / 100) x 0.35 = $840. $240,000 x 0.002 = $480. Answer: $2,100 deed stamp tax, $840 note stamp tax, $480 intangible tax, for $3,420 total.
How do we calculate area on the exam?
Area questions ask for square footage or acreage from given dimensions, then sometimes convert between the two. A rectangular lot measures 120 feet by 150 feet.
Formula: Area = length x width; acres = square feet / 43,560. Substitution: 120 x 150 = 18,000 square feet. 18,000 / 43,560. Answer: 18,000 square feet, or about 0.41 acres.
How do we work a seller’s net proceeds problem?
Net proceeds problems stack several deductions against the sale price, and the exam usually wants the running total, not just one line item. The $340,000 sale from our commission example above has a $210,000 mortgage payoff, the $1,810 tax proration credit to the buyer from above, and $2,500 in additional seller closing costs.
Formula: Net proceeds = sale price minus commission minus mortgage payoff minus prorations owed minus closing costs. Substitution: $340,000 minus $20,400 minus $210,000 minus $1,810 minus $2,500. Answer: $105,290 to the seller.
How is a PITI payment estimated?
PITI bundles principal, interest, taxes, and insurance into one monthly figure, and the exam usually gives you the loan terms and asks you to estimate the total. A $200,000 loan is fixed at 6.5 percent for 30 years, with estimated annual taxes of $3,660 and annual insurance of $1,440.
Formula: Monthly P&I from an amortization formula, plus (annual taxes / 12), plus (annual insurance / 12). Substitution: Monthly P&I on those terms works out to about $1,264. Taxes: $3,660 / 12 = $305. Insurance: $1,440 / 12 = $120. Answer: About $1,689 total monthly PITI ($1,264 + $305 + $120).
How do we calculate a capitalization rate?
Cap rate measures the return an income property generates relative to its price, and it’s one of the few math questions pulled from investment analysis rather than a residential closing. A rental property generates $18,000 in annual net operating income and is priced at $240,000.
Formula: Cap rate = net operating income / purchase price. Substitution: $18,000 / $240,000. Answer: 0.075, or a 7.5 percent cap rate.
How do discount points get calculated?
A discount point costs 1 percent of the loan amount and buys down the interest rate, and the exam usually just wants the dollar cost. A buyer pays 1.5 points on a $180,000 loan to lock a lower rate.
Formula: Point cost = loan amount x (points / 100). Substitution: $180,000 x 0.015. Answer: $2,700.
The ten problems, side by side
| # | Problem type | Formula | Answer |
|---|---|---|---|
| 1 | Commission | Price x rate | $20,400 |
| 2 | Commission split | Half x agent % | $6,120 |
| 3 | Loan-to-value | Loan / value | 80% |
| 4 | Tax proration | (Annual / 365) x days | $1,810 |
| 5 | Transfer tax | (Price / 100) x rate | $2,100 + $840 + $480 |
| 6 | Area | Length x width | 18,000 sq ft |
| 7 | Net proceeds | Price minus deductions | $105,290 |
| 8 | PITI | P&I + tax/12 + ins/12 | $1,689/mo |
| 9 | Cap rate | NOI / price | 7.5% |
| 10 | Discount points | Loan x points% | $2,700 |
Work all ten in order once, untimed, checking your process against the formula each time. Then run them again from memory with a five-minute clock and no notes. If problem five (transfer tax) or problem seven (net proceeds) slows you down, that’s normal, they stack three or more steps, and slowing down on multi-step problems while speeding up on single-step ones is exactly the pattern real exam data shows too.
Why these numbers, and not textbook round figures?
Most math guides use round numbers like $200,000 at 5 percent to make the arithmetic easy, which is exactly backward from what the real exam does. State exams pull odd purchase prices, mixed loan terms, and mid-month closing dates on purpose, because they’re testing whether you can find the right formula under realistic conditions, not whether you’ve memorized one clean example. Every problem above uses a number that doesn’t divide evenly, on purpose, so the process, not the arithmetic, is what you’re practicing.
Real estate math is roughly 6 to 10 percent of a state licensing exam’s total questions, but it drives more retakes than its share of points would suggest. A 2026 state-by-state pass rate analysis from Colibri Real Estate put the national first-time pass average at 61.4 percent, and calculation-heavy sections are consistently the category candidates flag as their weakest on post-exam diagnostic reports.
Practice these under real time pressure
Reading a worked solution is not the same skill as producing one cold, under a clock, with no memory of the steps to lean on. The AgentExamHub practice quiz tool includes a dedicated math section timed the way PSI and Pearson VUE actually run their calculation questions, so you’re building speed, not just recognition.
If you want every formula family drilled with multiple variations instead of one example each, the AgentExamHub free study guide includes a full math workbook section with answer keys showing every step, not just the final number.
FAQ
How much of the real estate exam is math? Typically 6 to 10 percent of total questions, depending on the state and testing vendor, though the exact share is published in your state’s candidate information bulletin. It’s a small slice of the exam but a common reason candidates fail a portion outright.
What formulas should we memorize first? Commission, loan-to-value, and proration cover the largest share of math questions on most state exams, so start there before moving to cap rate and discount points, which appear less often but still show up on most outlines.
Can we use a calculator during the math section? Most states allow a basic four-function calculator, either provided at the test center or brought by the candidate, but check your state’s bulletin since financial or programmable calculators are commonly restricted.
Do all states test the same math topics? The core formulas, commission, proration, loan-to-value, area, and transfer tax, appear almost everywhere because they’re part of everyday real estate practice, but the exact mix and difficulty vary by state, and some states weight prorations or transfer tax more heavily than others.
What’s the fastest way to stop missing proration questions? Convert everything to a daily rate first, then multiply by the exact number of days each party owned the property, counting carefully whether the closing day itself belongs to the buyer or seller under your state’s convention.
Bottom line: real estate exam math is short but unforgiving. Six or so formula families cover nearly everything tested, and the fastest way to stop missing points is working full problems start to finish, not memorizing formulas in isolation.