Real Estate Math for Texas Agents
Real estate math shows up throughout a transaction, from commissions and down payments to prorations and investment analysis. This chapter teaches the core formulas and shows how to apply them step by step using plain arithmetic. Mastering a few key relationships lets you handle most exam and real-world calculations with confidence. Always read each problem carefully to identify what is being asked and which numbers are the part, the whole, and the rate before you choose a formula.
Commissions and Splits
Most real estate math builds on one master relationship: part = whole x rate. In a commission problem, the whole is usually the sales price, the rate is the commission percentage expressed as a decimal, and the part is the commission dollars. The single most important habit is to convert every percentage to a decimal before you multiply by moving the decimal point two places to the left, so 6% becomes 0.06, 5.5% becomes 0.055, and 3% becomes 0.03; forgetting this step is the most common cause of wrong answers. To find a total commission, multiply the sales price by the rate. For example, on a $350,000 sale at a 6% total commission, the commission is $350,000 x 0.06 = $21,000. Commissions are then typically divided in stages, so work them one step at a time. First, split the total between the listing brokerage and the selling (buyer's) brokerage, which is often but not always 50/50; a 50/50 split of the $21,000 gives each brokerage $21,000 x 0.50 = $10,500. Second, apply the individual agent's split with their own brokerage to that brokerage's share. If the selling agent keeps 70% of their brokerage's portion, the agent earns $10,500 x 0.70 = $7,350, and the brokerage keeps the remaining $10,500 x 0.30 = $3,150. You can also work these problems backward. If you know an agent received $7,350 and kept 70% of the brokerage's half, you can reverse the steps: the brokerage's share was $7,350 / 0.70 = $10,500, the total commission was $10,500 / 0.50 = $21,000, and the sales price was $21,000 / 0.06 = $350,000. Remember that commission rates are always negotiable and are never set by law or by any association, so a problem will always give you the rate to use. A reliable exam technique is to write down what you are solving for, label each number as the part, the whole, or the rate, and then decide whether to multiply (when you have the whole and the rate) or divide (when you have the part and need the whole, or have the part and the whole and need the rate). Taking these problems in small, labeled steps prevents the mistakes that rushing causes.
Percentages, Down Payments, and Loan-to-Value
Percentage problems all use the same part = whole x rate relationship, so the skill is identifying which quantity is missing and rearranging: whole = part / rate, and rate = part / whole. Percentage change measures how much a value rose or fell relative to where it started, so divide the amount of change by the original value, not the new value. If a home rose from $250,000 to $300,000, the change is $50,000, and the percentage increase is $50,000 / $250,000 = 0.20, or 20%. If a value fell from $300,000 to $270,000, the change is $30,000 and the decrease is $30,000 / $300,000 = 0.10, or 10%. A down payment is simply a percentage of the purchase price, so multiply price by the down-payment rate: 15% down on a $280,000 home is $280,000 x 0.15 = $42,000, and the loan is the remaining $280,000 - $42,000 = $238,000. Loan-to-value, or LTV, is the loan amount divided by the value (or price, whichever is lower), expressed as a percentage, and it is the mirror image of the down payment because the down payment percentage plus the LTV percentage add up to 100%. On a $325,000 property with 80% LTV, the loan is $325,000 x 0.80 = $260,000 and the down payment is the remaining 20%, or $325,000 x 0.20 = $65,000. LTV matters in practice because a conventional loan above 80% LTV generally requires private mortgage insurance. A closely related and heavily tested type is the net-to-seller problem, where the seller wants to walk away with a certain amount after paying costs that are stated as a percentage of the sale price. Because those costs come out of the price, you cannot simply add them; instead divide the desired net by (100% minus the cost rate). To net $190,000 after paying 5% in costs, the price must be $190,000 / (1 - 0.05) = $190,000 / 0.95 = $200,000. You can check it: 5% of $200,000 is $10,000, and $200,000 - $10,000 = $190,000, which matches. Setting up the base value correctly, and dividing rather than adding on net problems, is the key to getting these right.
Area, Interest, and Property Tax
Area, interest, and tax problems each apply a simple formula to a base amount, and the main hazard is unit conversion, so always check what units the question wants. The area of a rectangle is length times width. A lot measuring 150 feet by 200 feet contains 150 x 200 = 30,000 square feet. For a triangle, the area is one-half the base times the height, so a triangular lot with a 100-foot base and 80-foot height is 0.5 x 100 x 80 = 4,000 square feet, and irregular shapes can be split into rectangles and triangles that you add together. The most important land conversion to memorize is that one acre equals 43,560 square feet; dividing a square-foot figure by 43,560 gives acres, so 87,120 square feet is 87,120 / 43,560 = 2 acres, and multiplying acres by 43,560 gives square feet. Simple interest is principal times the annual rate, and you divide by 12 to get a monthly figure. Annual interest on a $200,000 loan at 6% is $200,000 x 0.06 = $12,000, which is $12,000 / 12 = $1,000 per month; if a problem gives you the monthly interest and the rate, you can reverse it to find the principal by dividing. Property tax in Texas is often quoted as a rate per $100 of assessed value, so the method is to divide the value by 100 and then multiply by the rate. A property assessed at $180,000 taxed at $2.50 per $100 is ($180,000 / 100) x $2.50 = 1,800 x $2.50 = $4,500 per year. When a tax rate is instead given as a mill rate, remember that one mill is one-thousandth of a dollar, or $0.001, so a rate of 25 mills equals $0.025 per dollar of value, and $180,000 x 0.025 = $4,500, the same answer expressed differently. The disciplined approach for all three problem types is to write the formula, plug in the base amount, apply the rate, and then confirm your answer is in the units the question asked for, whether that is square feet, acres, a monthly dollar figure, or an annual tax bill. Careful unit tracking prevents most errors on this part of the exam.
Proration at Closing
Proration is the fair division of an ongoing expense, most often property taxes, between the seller and the buyer based on how much of the period each one owned the property. Getting proration right requires three steps: figure out who owes what, calculate a daily or monthly rate, and then multiply by the correct number of days or months. First, determine who owes. Texas property taxes are typically paid in arrears, meaning the bill for a year is not paid until the end of that year, so at a mid-year closing the seller has used the property for part of the year but has not yet paid those taxes. The seller therefore owes the buyer for the days the seller owned the property, because the buyer will receive and pay the full tax bill later. Second, calculate the rate. Many exams and closings use a 360-day year (a banker's year of twelve 30-day months) to keep the arithmetic clean, though some use the actual 365-day calendar, so read the problem to see which method to use. To get a daily rate, divide the annual expense by 360 (or by 365); to get a monthly rate, divide by 12. Third, multiply the rate by the seller's ownership period to find the seller's share. Suppose the annual taxes are $4,800 and the closing is exactly at mid-year, so the seller owned the property for six months. Using the monthly method, the monthly rate is $4,800 / 12 = $400, and the seller's six-month share is $400 x 6 = $2,400. Using the daily method with a 360-day year, the daily rate is $4,800 / 360 = $13.333 per day, and 180 days gives 180 x $13.333 = $2,400, the same result. Finally, apply the amounts to the closing statement as debits and credits. Because Texas taxes are paid in arrears and the buyer will pay the whole bill after closing, the seller's owed portion is charged to the seller (a debit to the seller) and given to the buyer (a credit to the buyer) so the buyer is reimbursed for the seller's share. For prepaid items the seller already paid beyond closing, the direction reverses and the seller is credited. The reliable habit is to identify the payment timing, choose the day-count method the problem specifies, compute the rate, multiply by the correct period, and then place the amount as a debit and a matching credit.
Investment and Value Calculations
Investors and appraisers translate a property's income into an estimate of value, and a few formulas cover most exam questions, with consistency of units (annual versus monthly) being the recurring trap. The capitalization rate ties income to value through the relationship value = net operating income / cap rate, where net operating income (NOI) is the annual income remaining after operating expenses but before mortgage payments. If a property produces $24,000 of NOI and investors expect an 8% cap rate, the value is $24,000 / 0.08 = $300,000. The same triangle rearranges: if you know value and NOI, the cap rate is NOI / value ($24,000 / $300,000 = 0.08, or 8%), and if you know value and cap rate, the NOI is value x cap rate. Note that a higher cap rate generally implies more risk and a lower value for the same income, while a lower cap rate implies less risk and a higher value. The gross rent multiplier, or GRM, is a quicker rule of thumb that relates value to gross rent rather than to net income, using value = gross rent x GRM. If comparable sales suggest a GRM of 12 and the subject collects $18,000 in annual rent, the indicated value is $18,000 x 12 = $216,000; you can also derive the GRM from a comparable by dividing its price by its rent. Because some problems quote monthly rent, convert it to annual (multiply by 12) before applying an annual GRM, or make sure the multiplier matches the rent period the problem uses. A cost-based estimate multiplies the building area by a cost per square foot: a 2,000-square-foot home at $120 per square foot indicates $2,000 x $120 = $240,000 for the improvements, to which land value would be added under the cost approach. Return on investment is another common calculation, found by dividing annual net income by the amount invested; $30,000 of annual net income on a $375,000 investment is $30,000 / $375,000 = 0.08, or an 8% return. The single most important discipline across all of these is to keep your time units consistent: if the rate or multiplier is annual, the income must be annual, so convert monthly figures to yearly (or the reverse) before you multiply or divide. Writing the formula first, labeling each number, and checking that the units line up will carry you through nearly every investment problem on the exam.
Last updated: September 2026
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