Real Estate Math: Practice Questions & Explanations

Step by step: total commission = 6% of $400,000 = $24,000. Split equally between listing and buyer brokerages = $12,000 to each brokerage. Each brokerage pays its agent 50% = $6,000 to the listing agent. The buyer's agent receives the same amount from their brokerage's share. Real estate math questions reward careful step-by-step work because compound calculations are easy to short-circuit. Always identify what is being asked (commission, net to seller, gross sales price), apply percentages in the correct order, and check that your answer is reasonable. The standard real estate commission split (50/50 between brokerages, 50/50 between brokerage and agent) is a common assumption on exams, but actual splits vary widely.

GRM (Gross Rent Multiplier) method: Property Value = Gross Monthly Rent × GRM. So $2,000 × 150 = $300,000. The GRM is a quick approximation used for small income properties. It is a ratio derived from comparable sales in the market: take recent sale price ÷ monthly rent for several comparables to find typical GRMs. A higher GRM means properties are selling for more relative to their rent; lower GRM means rents are higher relative to price. GRM ignores expenses, vacancy, and financing — it is a back-of-envelope tool, not a full investment analysis. For more rigorous valuation of income property, appraisers use the income capitalization approach with NOI (Net Operating Income) and a cap rate.

Down payment: 20% × $250,000 = $50,000. Loan amount = purchase price − down payment = $250,000 − $50,000 = $200,000. The 20% down payment is significant in residential financing because it is typically the threshold at which private mortgage insurance (PMI) is no longer required on conventional loans. Borrowers with less than 20% down can still get conventional loans but pay PMI premiums until they reach 20% equity, or they use FHA, VA, or USDA loan programs with different rules. A higher down payment also reduces the monthly payment (smaller loan amount, less interest over time) and improves the borrower's debt-to-income ratio for qualification.

Monthly interest = (Loan Balance × Annual Rate) ÷ 12. So $300,000 × 0.06 ÷ 12 = $300,000 × 0.005 = $1,500. The first month's interest is $1,500. The total monthly payment of principal and interest (P&I) on a 30-year $300,000 loan at 6% is roughly $1,799, of which $1,500 is interest and about $299 is principal in the first month. Over time, more of each payment goes to principal and less to interest as the balance amortizes. By month 240 of a 30-year loan, the split inverts. Real estate exams often test simple interest calculations like this; mortgage payment calculations using amortization tables are more complex but less common on the salesperson exam. Always remember: monthly rate = annual rate ÷ 12.

Step 1: Total commission = 6% × $425,000 = $25,500. Step 2: Listing brokerage's share = 50% × $25,500 = $12,750. Step 3: Listing agent's share = 60% × $12,750 = $7,650. Commission calculation questions follow this structure: total commission → broker's split → agent's split. The exam uses various split percentages — know the formula: (sale price × commission rate) × broker split × agent split.

Property tax calculation: Tax = (Assessed Value ÷ $1,000) × Tax Rate. Tax = ($180,000 ÷ $1,000) × $15 = 180 × $15 = $2,700. This is the standard mill-rate calculation. A mill rate (or millage) represents tax per $1,000 of assessed value. $15 per $1,000 = 15 mills. Annual property tax = $2,700. Variations on the exam: assessed value may be expressed as a percentage of market value (e.g., assessed at 80% of $225,000 = $180,000 assessed value); the mill rate may be expressed as decimals (0.015 × $180,000 = $2,700 — same result).

First find the total commission: $360,000 × 6% = $360,000 × 0.06 = $21,600. The two brokerages split it equally, so each receives $21,600 ÷ 2 = $10,800. (Any further split between a brokerage and its individual agent would come out of that brokerage's share and is a separate calculation.) Commission problems are a staple of the real estate math section: convert the percentage to a decimal, multiply by the sale price for the total, then divide according to the split described. Watch carefully for whether the question asks for the total commission, one brokerage's share, or an individual agent's share.

First find the area in square feet: 80 ft × 150 ft = 12,000 sq ft. Then convert to acres by dividing by 43,560 sq ft per acre: 12,000 ÷ 43,560 ≈ 0.275, which rounds to about 0.28 acre. Area-and-acreage problems are common on the math portion, and the key fact to memorize is that one acre equals 43,560 square feet. The method is always the same: compute the area in square feet (length × width for a rectangle), then divide by 43,560 to express it in acres. Keeping the conversion factor memorized lets you handle lot-size and land questions quickly.