Math makes up 10–15% of the real estate exam. There are only twelve problem types that recur. Memorize the setup for each one and the category stops being intimidating.
1. Commission
Given sale price, commission rate, and an agent's split, calculate the agent's gross. Example: $420,000 sale × 6% total commission × 50% brokerage split × 70% agent split = $8,820. Always sequence the percentages. Don't add rates.
2. Prorations
Taxes, rent, HOA dues, or insurance split between buyer and seller at closing. Example: $3,650 annual tax / 365 days × 90 days = $900 seller's portion if the seller owned the property for 90 days of the year. Some states use a 360-day banker's year — memorize your state's convention.
3. Loan-to-value ratio (LTV)
LTV = loan amount ÷ appraised value or sale price (whichever is lower). A $340,000 loan on a $400,000 appraisal = 85% LTV. LTV controls PMI thresholds and lender pricing.
4. Qualifying ratios
Front-end (housing expense) ratio = PITI ÷ gross monthly income. Back-end (total debt) ratio = (PITI + other debt payments) ÷ gross income. Exam questions typically give you a limit (28/36 or 31/43) and ask whether a borrower qualifies.
5. Ad valorem (property) tax
Assessed value × mill rate (per $1,000 of value) or tax rate. A $250,000 assessment at 25 mills = $6,250 annual tax. Sometimes the problem gives you assessed as a percentage of market value — read carefully.
6. Appreciation and depreciation
Given a purchase price and annual rate, calculate today's value. Note whether the rate is straight-line (simple) or compound (multiplicative). Exam questions almost always specify.
7. Net operating income (NOI) and cap rate
NOI = gross income − operating expenses (not debt service). Cap rate = NOI ÷ property value. Given any two of the three, solve for the third. This one shows up on income property problems and trips candidates who confuse operating expenses with mortgage payments.
8. Net listings
Given a seller's minimum take-home and a target gross, calculate the sale price. Seller wants $380,000 net; closing costs are $12,000; commission is 6%. Gross = ($380,000 + $12,000) ÷ (1 − 0.06) = $417,021. The "divide by (1 − rate)" step is the one people miss.
9. Mortgage interest and amortization
Basic interest for a given period: principal × rate × time. Early-payment math asks how much of the first payment is interest versus principal (most of it is interest on a 30-year loan). Full amortization tables aren't required on the exam.
10. Legal descriptions
Metes and bounds, rectangular survey (sections, townships, ranges), and lot-and-block. A section = 640 acres; a quarter-section = 160; a quarter-quarter = 40. If a question gives you "the NE¼ of the SW¼ of Section 14," that's 40 acres.
11. Square footage and area
Rectangular lots are length × width. Irregular lots are sometimes split into rectangles and triangles; triangle area = ½ × base × height. 1 acre = 43,560 square feet.
12. Transfer tax
State-specific. Rate × sale price, sometimes with a rounding rule (per $500, per $100). A $420,000 sale at $0.55 per $500 = 420,000 ÷ 500 × 0.55 = $462.
How to study this
Don't memorize formulas. Memorize the setup. Each problem type has one characteristic signal in the question — "what's the agent's share" means commission, "assessed value" means tax, "NOI" means cap rate. Identify the type in the first five seconds, and the math follows.