Real Estate Exam Math: Every Calculation on the National Outline, With Worked Examples

What the national outlines list

Math is a small area by item count but it reaches into valuation, financing and settlement too. Pearson VUE's outline, effective April 1, 2025, gives Real Estate Math Calculations 7 of 80 scored items, 4 of them application and 3 analysis, with no recall items at all. PSI weights Real Estate Calculations at 7% of the salesperson exam.

Two facts to memorize and three rules the question gives you

Pearson VUE's outline lists two facts that are "NOT available at the test center and SHOULD be memorized": 43,560 square feet per acre and 5,280 feet per mile. For prorations, the question itself will say:

• whether to use a 360-day or 365-day year
• whether the day of closing belongs to the buyer or the seller

and calculations are rounded using standard rounding rules. Legal-description questions also use the rectangular survey's numbers: a standard section is about 1 mile square and contains 640 acres, and a quarter section is 160 acres.

Calculator rules depend on your state. Pearson VUE's Arizona handbook allows a silent, hand-held, nonprinting calculator without an alphabetic keypad, and its Texas handbook allows financial calculators without alpha characters and says calculators are not provided. PSI's New Hampshire bulletin provides an online calculator or lets you bring a silent non-programmable one, while PSI's Virginia bulletin lists handheld calculators among prohibited items. The exam day guide has the full list, including California's.

Worked examples for each calculation

Every example below is Passy's own, with round numbers so you can follow the method. Recompute each one yourself before you move on.

Area and acreage

A rectangular lot measures 330 feet by 660 feet. Its area is 330 × 660 = 217,800 square feet, and 217,800 ÷ 43,560 = 5 acres. At $12,000 per acre, the land is worth 5 × $12,000 = $60,000.

For an L-shaped house, split the shape into rectangles: a 40 × 30 section (1,200 square feet) plus a 20 × 15 wing (300 square feet) is 1,500 square feet. A quarter mile of road frontage is 5,280 ÷ 4 = 1,320 feet.

Commission and compensation

A home sells for $380,000 at a 6% commission: $380,000 × 0.06 = $22,800. If the listing brokerage keeps half, it receives $11,400. If the listing agent's split with that brokerage is 70%, the agent earns $11,400 × 0.70 = $7,980. Work splits one layer at a time, and note whose share the question asks for.

Value, income and property tax

• Capitalization rate. A building has gross potential rent of $96,000, a 5% vacancy allowance and $27,840 in operating expenses. Effective gross income is $96,000 × 0.95 = $91,200, and net operating income is $91,200 − $27,840 = $63,360. At an 8% cap rate, value = $63,360 ÷ 0.08 = $792,000.
• Gross rent multiplier. A rental sold for $240,000 and rents for $2,000 a month, a monthly multiplier of $240,000 ÷ $2,000 = 120. A similar home renting for $2,100 at the same multiplier is worth about $2,100 × 120 = $252,000.
• Cost approach. A building would cost $300,000 to build new and is 10 years into a 50-year economic life, so straight-line depreciation is 10 ÷ 50 = 20%, or $60,000. Add land worth $90,000: $300,000 − $60,000 + $90,000 = $330,000.
• Assessed value and tax. A home's market value is $300,000 and the assessment ratio is 40%, so its assessed value is $120,000. At a rate of 25 mills, meaning $25 per $1,000 of assessed value, the annual tax is 120 × $25 = $3,000.

Loan financing costs and PITI

• Loan-to-value. A buyer borrows $288,000 on a $360,000 home: $288,000 ÷ $360,000 = 80% LTV, with a $72,000 down payment.
• Discount points. The CFPB explains that one point equals one percent of the loan amount, so 2 points on $288,000 cost $5,760.
• Interest. At 6.75%, the first month's interest is $288,000 × 0.0675 ÷ 12 = $1,620.
• Payment. On a 30-year fixed loan, the standard amortization formula gives principal and interest of about $1,867.96 a month. Add annual taxes of $4,800 ($400 a month) and insurance of $1,500 ($125 a month), and PITI is $2,392.96.

PSI's outline lists a "PITI payments estimate given loan rate and term," so be ready either to compute the payment or to use one the question supplies.

Settlement: net to the seller and cost to the buyer

• Price needed to net a target. A seller wants $300,000 after a 6% commission and $4,500 of other costs. Divide by what the seller keeps after commission: ($300,000 + $4,500) ÷ 0.94 = $323,936.17. Check: $323,936.17 − 6% ($19,436.17) − $4,500 = $300,000.
• Cash the buyer brings. A $360,000 purchase with 20% down ($72,000), $9,500 of closing costs and $2,100 of prepaid items, minus a $10,000 earnest money deposit and a $3,000 seller credit: $72,000 + $9,500 + $2,100 − $10,000 − $3,000 = $70,600.
• Transfer tax. Rates differ from place to place, so the question will give one. With an illustrative rate of $1.00 per $500 of price or fraction of $500, a $327,250 sale is 654.5 units, rounded up to 655, for a tax of $655.

Prorations

Taxes paid in arrears. A sale closes June 15. The year's property tax of $4,380 hasn't been paid yet and the buyer will pay it later. Use a 365-day year; the buyer owns the day of closing. The daily rate is $4,380 ÷ 365 = $12. The seller owns January 1 through June 14: 31 + 28 + 31 + 30 + 31 + 14 = 165 days, so the seller's share is 165 × $12 = $1,980. That is a credit to the buyer and a debit to the seller.

Rent collected in advance. The seller collected June's rent of $1,800 on June 1. Closing is June 15, the buyer owns the day of closing, and the question says to use a 360-day year (30-day months). The daily rent is $1,800 ÷ 30 = $60. The buyer owns June 15 through 30, 16 days, so the seller credits the buyer 16 × $60 = $960.

The two examples move money in the same direction for different reasons: in the first the seller hasn't paid an expense yet, in the second the seller has collected income that belongs partly to the buyer.

Investment and property management

• Equity. A home worth $410,000 with a $265,000 loan balance has $145,000 of equity.
• Appreciation. A home bought for $250,000 and now worth $287,500 has appreciated ($287,500 − $250,000) ÷ $250,000 = 15%.
• Return on investment. An investor who receives $9,000 a year on $90,000 invested earns $9,000 ÷ $90,000 = 10%.
• Management fee. Twelve units rent for $1,650 a month at 95% occupancy, so collected rent is $1,650 × 12 × 12 × 0.95 = $225,720 a year. An 8% management fee on collected rent is $18,057.60.

To see where math meets valuation, math explanations planned to rework each step cover cap-rate, commission and proration problems in the planned prep.

A Passy practice item on net to the seller

A seller wants to walk away with $280,000. The commission is 7% of the sale price, and the seller's other closing costs are $3,650. What is the lowest sale price, to the nearest dollar, that meets the seller's goal?

• A. $305,000
• B. $303,250
• C. $301,075
• D. $283,650

Answer: A. ($280,000 + $3,650) ÷ 0.93 = $305,000, and 7% of $305,000 is $21,350, which leaves exactly $280,000 after the $3,650 of costs. Option B adds 7% of $280,000 plus the costs, which understates the price because the commission is charged on the higher sale price. Option C ignores the closing costs ($280,000 ÷ 0.93), and option D ignores the commission.

If you picked B, you made the setup error this item is designed to catch. Fix It's planned retry list for missed calculations is built to bring a question like this back until you solve it cleanly.

Practicing math so it holds up under time pressure

1. Write the formula in words first, such as "value equals income divided by rate," then substitute numbers.
2. Label units on every line: dollars per day, square feet, months. Mixed-up units are an easy way to land on a wrong option.
3. Check with the reverse operation, the way the net-to-seller example does.
4. Mix math into every study day. With only 7 dedicated items, math rarely deserves its own week, but the same skills earn points in valuation and financing questions.

The study guide shows where math fits in a weekly plan, and the financing guide explains the loan terms behind the numbers. For volume, 55 math questions planned for launch can be practiced as an area of their own, and the free practice questions include commission-split and proration items you can try now.