Real Estate Mathematics
Real estate math appears throughout the exam and in daily practice, from calculating commissions to prorating taxes at closing. This chapter reviews the core calculations you must master: commissions and splits, financing math, area and land measurements, prorations, and property taxes. Practice converting percentages to decimals and following each formula step by step.
Commissions and Splits
Commission problems are the most common math items on the exam, and they all reduce to the base formula: commission = sale price × commission rate, with the rate written as a decimal. To convert a percentage to a decimal, move the decimal point two places to the left, so 6% becomes 0.06. If a home sells for $325,000 at a 6% total commission, the commission is 325,000 × 0.06 = $19,500. Splits are then applied in order. Suppose the listing brokerage and the selling (cooperating) brokerage split that total evenly: each brokerage receives 19,500 × 0.50 = $9,750. If the listing agent's agreement pays the agent 60% of what the brokerage keeps, the agent earns 9,750 × 0.60 = $5,850, and the brokerage retains 9,750 − 5,850 = $3,900. The key discipline is to work from the whole to the part: find the total commission first, divide it between the sides, then divide each side between brokerage and agent. A second common variation is the seller's-net problem, which runs the formula backward. If a seller wants to net a specific amount after paying commission and no other costs, the sale price = net ÷ (1 − commission rate). To net $188,000 at a 6% commission, the required price is 188,000 ÷ (1 − 0.06) = 188,000 ÷ 0.94 = $200,000; check it: 200,000 × 0.06 = $12,000 commission, and 200,000 − 12,000 = $188,000. Do not make the frequent error of multiplying the net by the rate and adding it back, which understates the price. Always confirm what the rate applies to (usually the gross sale price), keep percentages in decimal form, and verify each step by plugging the answer back into the original relationship. These same techniques handle referral fees and bonus splits, which are simply additional multiplications layered on the total.
Financing Math
Financing math turns on a handful of relationships that the exam recombines. A down payment is a percentage of the purchase price, and the loan is the remainder: on a $250,000 home with 20% down, the down payment is 250,000 × 0.20 = $50,000 and the loan is 250,000 − 50,000 = $200,000. The loan-to-value ratio (LTV) compares the loan to the lesser of price or appraised value: LTV = loan ÷ value. A $180,000 loan on a $240,000 property is 180,000 ÷ 240,000 = 0.75, or 75% LTV. Turned around, the maximum loan equals value × LTV, so at 80% LTV a $240,000 property supports 240,000 × 0.80 = $192,000. Simple interest, used for most exam problems, is interest = principal × rate × time. One year of interest on a $200,000 loan at 5% is 200,000 × 0.05 = $10,000, and one month is 10,000 ÷ 12 = $833.33. To find a monthly interest-only payment, take the annual interest and divide by 12. Discount points are a form of prepaid interest, with each point equal to 1% of the loan amount, so two points on a $200,000 loan cost 200,000 × 0.02 = $4,000. A qualifying problem may ask what payment a borrower can support: multiply monthly income by the allowed housing ratio. Keep every percentage in decimal form, track whether a figure applies to price or to value, and confirm whether the problem wants annual or monthly interest. As always in real estate math, plug the answer back into the relationship to verify it — a $4,000 point cost should equal exactly 2% of the $200,000 loan — and remember that any specific loan limits, insurance rates, or qualifying ratios used in practice must be verified with the lender.
Area and Land Measurement
Area problems support both valuation and land descriptions, and most reduce to the rectangle. The area of a rectangle equals length × width, expressed in square feet when both dimensions are in feet: a lot 80 feet by 120 feet contains 80 × 120 = 9,600 square feet. To handle an L-shaped building or lot, divide it into rectangles, compute each, and add the pieces; for a triangle such as a corner lot, use area = ½ × base × height. Memorize the key conversion: one acre equals 43,560 square feet. To convert square feet to acres, divide by 43,560, so a 21,780-square-foot parcel is 21,780 ÷ 43,560 = 0.5 acre. To go the other way, multiply acres by 43,560; a 3-acre tract is 3 × 43,560 = 130,680 square feet. Cost and value estimates often multiply area by a rate per square foot: a 2,000-square-foot house valued at $150 per square foot indicates 2,000 × 150 = $300,000, and construction estimated at $120 per square foot for the same house costs 2,000 × 120 = $240,000. Volume problems, for warehouse or concrete questions, multiply length × width × height in cubic feet. Florida land can also be described by the rectangular (government) survey system, in which a section is one square mile containing 640 acres; a quarter-section is 640 ÷ 4 = 160 acres, and a quarter of a quarter is 160 ÷ 4 = 40 acres. The essential habit is to keep all measurements in consistent units before multiplying — convert yards or inches to feet first — and to label your result as square feet, acres, or dollars so that you answer the question actually asked. Verify any unusual local measurement conventions where they apply.
Prorations at Closing
Prorations divide a shared, continuing expense fairly between buyer and seller at closing so that each pays only for the days they own the property. Property taxes are the classic example, and in Florida taxes are paid in arrears — billed near the end of the year for that year — so at a mid-year closing the seller has used the property for months without yet paying the tax, and the seller typically credits the buyer at closing for the seller's share, which the buyer will later pay when the bill comes due. To prorate, first find the daily rate by dividing the annual amount by the number of days in the year, then multiply by the number of days each party is responsible. Two conventions exist: the 365-day (actual, or exact) method and the 360-day (banker's, or statutory) method that treats each month as 30 days. Using the 365-day method, suppose annual taxes are $3,650 and the seller owned the property for the first 120 days of the year through the day before closing. The daily rate is 3,650 ÷ 365 = $10.00 per day, and the seller's share is 10.00 × 120 = $1,200, credited to the buyer. Under the 360-day method the same $3,650 gives a daily rate of 3,650 ÷ 360 = $10.14 per day, which is why the problem must tell you which convention to use. Watch two details: determine which party is charged for the day of closing, which is set by contract or local custom, and confirm whether the expense is paid in arrears (seller credits buyer) or in advance, such as prepaid insurance or association dues (buyer reimburses seller). Rent on an income property is usually prorated with the seller keeping rent through the day before closing and crediting the buyer for the unused balance of the month. Always state your day-count assumption and verify local custom.
Property Taxes and Percentages
Property taxes are commonly expressed in mills, and a mill is one one-thousandth of a dollar, or $1 of tax per $1,000 of taxable value. To apply a millage rate, divide the taxable (assessed) value by 1,000 and multiply by the number of mills. On a property with a taxable value of $200,000 taxed at 20 mills, the tax is (200,000 ÷ 1,000) × 20 = 200 × 20 = $4,000. Equivalently, 20 mills is a rate of 0.020, so 200,000 × 0.020 = $4,000. In Florida the taxable value is not necessarily the market value: the county property appraiser sets an assessed value, then subtracts exemptions such as the homestead exemption to reach taxable value, and the Save Our Homes cap limits how fast a homestead's assessed value can rise. Because exemption amounts and caps change, verify current figures with the county property appraiser. Percentage-change problems appear throughout real estate: the percent change equals the amount of change divided by the original value. A property that rose from $250,000 to $280,000 changed by 280,000 − 250,000 = $30,000, and 30,000 ÷ 250,000 = 0.12, a 12% increase. To find an original value after a known percentage change, divide the new value by (1 + the rate) for an increase or (1 − the rate) for a decrease; a value that is 112% of the original and now stands at $280,000 started at 280,000 ÷ 1.12 = $250,000. Keep straight whether a problem gives you assessed value or market value, and use the figure the problem supplies. The recurring exam skills are converting among mills, decimals, and percentages, and always dividing the change by the original — not the new — amount. Confirm current millage and exemption details locally before advising a client.
Last updated: September 2026
练习一直免费。完整的 Florida Real Estate Sales Associate Exam 学习指南是知识本身,从头到尾讲清楚 —— 可下载的 PDF + EPUB,永久归你。